When the text was translated by a Chinese guy on GAF (the text in the OP used Google translate), the word console was used. Not sure how accurate that is, but either way, if carts are to be used for the console, I would think it's so that people will be able to use it in either the console or the handheld. If the console uses disc media, you wont be able to put it into the handheld. (Unless Nintendo come up with a smaller sized disc, but I don't think thats a good idea).

I wouldn't dismiss the possibility of digital-only, but I don't find it realistic today, or a successful strategy if Nintendo choses to go that route.
Their prevous console had a bare minimum of storage space, and the people who wanted digital only would have to buy an externnal HDD. It was a similar situation on 3DS. Going from that directly to digital-only doesn't sound likely to me. Even Sony and MS, who have been accomodating towards their digital userbase for the past 10 years, wouldn't do that. MS certainly wanted to "ease" people into it with their DRM policies. But even amidst all that, their games would still be sold physically as well.

The answer to offering some things in digital form only would be to offer some things in digital form only. Not everything.
You can still buy movies, books or even music in physical form. There may be some exceptions, but that's not the norm. Even in the music industry, the revenue for digital music didn't pass the revenue for physical format sales until 2015. And it wasn't by a long shot. $6.85 billion vs $6.82 billion.
So that's still around 50/50.
In the console industry, we're looking at something like a 20/80 split. And those 20% don't translate into 20% of people who buy digital only. I buy some games digitally, so I factor into that number as well.

As for what Miyamoto said, that the unified platform came to light because of digital downloads is your interpritation. What he said was that it opens up the ability for multi-platform digital downloads. Which already exists today between systems that do not have a unified platform. I interpret this as one factor they intend to make use of for their unified platform. Not that this means it revolvs around digital media only. And the reason I think he used this particular example is because it's something that exists today so that people can relate to the situation better. Namely the other parts you highlighted. Why isn't this the case for most digital downloads? He highlights the issue of how each version of the game has to be reprogrammed to fit the different architecture and specs of the different platforms. When you download Resident Evil Remake for PS3, it also lets you download the game for PS4. But that's not the same version of the game. It's another version developed separately and specifically for PS4. And that's what I think he is highlighting here. With a unified platform sharing the same type of architecture, this wouldn't be a concern, and the games could be adjusted as simply as they can between two PC's with different specs.
The reason I believe he used digital downloads as an example is because they are currently the only form of "cross-platform buy" on consoles/handhelds today. Nintendo and Sony console storage media have never been compatible with their handheld system. And there has never been a reason for it, since the the games wouldn't work natively on the other system anyway.

When people buy physical, they tend to do so out of preference. And the reasons for that can vary a lot. It's not that most of them are unaware that they can opt to go digital. The question is how many of them can be forced into digital only. If it was a simple matter, Sony, MS, the music, movie and book industry, etc, would have done so already. I agree that third parties would love digital only. No storage or shelf space needed, no manufacturing costs, low distribusion cost, etc. Yet physical still remains an option that's very commonly chosen.
Steam have been successful in this, but this is the result of many years of making the transition, along with very low sale prices even for new games, and all the while physical copies on PC games still exist for the most part for people who want to go that route.
We saw what happened when MS even tried to force people into their DRM plan, which had everything to do with moving towards digital only down the line. PS4 pre-orders ran circles around XB1, and they're still feeling the effects of the backlash today, in spite of dropping all those plans.

Digital media for portable music meant not having to lug around those huge portable CD players, or the casette tape players that couldn't skip tracks. Music would also lag when you made sudden movements with a portable CD player, making it very unpracticle for having with your when you're out running, besides its huge size. Along with being able to easily download your music for free, these conveniences were the biggest benefits from MP3 players.
Not much of this applies to consoles or handhelds, aside from being able to carry multiple games with you on a handheld gaming device.

So of course people will prefer the format that doesn't force them to lug around huge CD players or cassette tape players with all the drawbacks that came with them. There was no reason to sell anything but digital for mp3 players. Even for home use, mp3 is very convenient nowadays.
That said, as I already mentioned, people still buy physical albums in droves. Just not to bring it with them on the go.

Another big benefit from mp3 purchases is being able to pick and chose exactly which songs you want from an album, and which ones you don't want. You may only be interested in three tracks from Kanye's new album. Ok, 3 dollars. Previously you could buy the singles released from these artists, but they may not be all the tracks you want from the album.
While there are some video games sold in an episodic manner, or have extra DLC content, there's no directly similar benefit to be found in videogames since most games are designed in a way where just playing one small portion of it without the context of the rest doesn't give the experience you expect from a game.

Obviously, we both know all this, and you've still formed your opinion around this and believe Nintendo will go all digital.
For me, these things tell me that digital-only would be a big mistake, and I'm not expecting it for the NX.

But there is one thing you said which I don't understand, that maybe you could explain to me?

Why would you gain consumers by limiting their purchase options to digital only, rather than offering both options (physical or digital)?
I don't see anything being gained from excluding the option of physical purchases in terms of consumers. It's not like someone will brush off a game that's available in both physical and digital form, but then all of a sudden be interested in it if it's only available in digital form. In that sense it's certain that they will only lose consumers, when considering this move alone. Not gain a single one.
The only gains to be made here when it comes to the consumers will come from the other aspects of NX and how they handle their games. Will they work on multiple platforms? Etc. But as mentioned, this is possible with both physical and digital games being made available.

Wait, do people still actually buy CDs though? Genuinely curious about this. I wouldn't even know where to buy a CD nowadays lol.

It's posible but unlikely for this year as AMD are apparently conscentrating on ZEN first.

No, it's understandable. A side effect of coming into the discussion late is the wall of text. lol We've never had this discussion though, so I wanted to at least express why I've reached the conclusions I have had on this matter. I think we have discussed things enough times to know that the other person has probably done their reasearch well enough to not change their mind, so there wouldn't be much point to the counter-counter-counter argument replies other than perhaps providing some info the other may have missed. I appreciate the notice though, and that you read it.

Although I'm curious about two things.
One is the last question I brought up. I'm assuming I either missunderstood you, or when you said "this move", you weren't specifically refering to just the digital only aspect, but Nintendo's plan with the NX as a whole?
Or perhaps I'm missing something. Are there any benefits for the consumers that are only possible with digital-only?
Because the only direct benefits I see from digital-only as opposed to digital and physical, is for the devolpers/publishers regarding logistics. Then it becomes a question of whether or not the developers/publishers want to pass on the savings to the consumers by offering cheaper prices. It's not a guarantee, but it's certainly a possibility.

The second thing is regarding your interpretation of what Miyamoto meant with his statement.
Are you sure that your interpretation is the only plausible one, or could mine also be possible?

You don't have to go into detail explaining why if you don't want to. A simple Yes or No will suffice as well.
I just wanted to know because you sounded very certain, and I'm curious how dead set you are on that.

But how exactly? PC games have shipped physical media for decades with assets for different settings, so why would it be a problem for NX?

I don't understand your logic.

If I bought a physical PC game in the past, the same copy could run at different settings on my own PC and the PCs of my friends. Or if I upgraded my PC, I could switch to higher settings without having to buy the game a second time. It all came on the same disc, after all.

Regardless of the NX device you plugged your card into, the device would recognize which assets and features it had to access from the card in order to offer the optimized experience.