How many times has Nintendo really offered hardware that could support modern games? After the GameCube (which got a fair bit of 3rd party support), you had Wii U, which flopped market wise because fickle casuals didn't want to buy game consoles anymore, but even that still had IP like Call of Duty and Assassin's Creed on it. 

Switch is really the first time that Nintendo's had a successful game product that has market demographics that fall in line with the types of games many developers make (ie: not soccer moms or kids mainly interested in dance/fitness games). 

Again it's not about having 500000 third party games and suddenly competing with Sony/MS, a Switch Pro can eventually become the main Switch that's sold and that can offer the ability for a few devs to offer up some of the more popular games in the industry if they wish. And Nintendo gets a higher end premium model that they can maintain a higher price point for ($300-$350) which is lucrative from a business end point. 

The only people who "lose" are those tiny minority on internet message boards who will cry about a new setup different from the 1980s way of doing things, and even they, the moment they see Resident Evil 2 Remake or Kingdom Hearts 3 or Elder Scrolls VI running on a Switch model will probably abruptly swallow their pride and go "oh cool, now that I see that, I want one". That allows happens. Describe a hybrid console here 3 years ago and half the board would cry bloody murder and say "no way! I want a distinct Nintendo console and portable, that's how its always been!", then show them the trailer for it and 5 minutes later "hey, you know this actually looks pretty neat, I'm buying one". 

The Switch is modern hardware capable of running many third party games, and it's still missing out on plenty it could viably handle. A Switch Pro won't suddenly get an avalanche of third party games like RE2R , KH3, or ES6, just like the current Switch is still missing RE7, GTA5, Overwatch, Spyro Reignited, etc.

Pretty sure Spyro is coming, Overwatch may happen too. RE7 is on the system but its streaming only, which means Capcom wants to offer it, they just don't want the headache of porting it. If the chip was more equivalent it probably is on the system now with RE2 Remake coming too. GTA5 is probably a no go because Rockstar makes their real $$$ off the online portion of the game and that portion of the game would have problems running on the current Switch (they dumped PS3/360 support for a reason). And who cares if not every developer supports, some would, and Nintendo only needs "some", it doesn't need 800 third party games added per year.

There are only really maybe 20 third party IP that really matter, if Nintendo could get even 7-8 of them that aren't on Switch now, that's a fair positive and helps grow the brand, and a Pro model is going to happen anyway most likely so why not get a little extra content. 

When has a stronger hardware model of an existing system ever resulted in a significant influx of meaningful third party support though? Much less on a Nintendo system?

Sega CD had quite a bit of software, it's kind of irrelevant because there's never really be a hardware like Switch which was so suited to following the Apple model of hardware revisions. The business of the 80s/90s/and even 2000s is in the past. 15 Years ago there wouldn't be a PS2 Pro either. 

The Sega CD was a massive failure.

30 years ago when the majority of the market was kids, sure. 

The PC has had a similar kind of setup of never ending generation/no real generation dilineation for many decades too and has done well. 

If you're selling only to kids it can be a problem, but the industry has grown up since then, even Nintendo's fanbase is majority adult today. 

There's still no indication that third parties would be any more willing to develop for a Switch Pro than they are for the current Switch.

We'll see, you can't know that because you can't read the mind of every single third party developer. 

Embracing a PC like setup where there is no real generations personally I think is smart and in the *long run* consumers will also see it as a positive and not want to go back to the old model. And getting in on that "Pro money" model that Apple/Samsung/Sony/Microsoft all make good $$$$ from is something Nintendo is going to end up doing most likely regardless of a few people on an internet message board complaining about it.

The reality is a 2-3x style "Pro upgrade" of a Switch simply would allow a lot of games that would be a real pain in the ass or impossible to port to the old Switch to become reasonable feasible on the Pro model. Some third parties will likely bite on that proposition and Nintendo won't stop them.