First to be clear (consider this a disclaimer), I am not suggesting that they do not have support for a disc drive at all. As theer are ways that a disc drive a beneficial and going all digital or even switching to carts won't circumvent those benefits. Now onto the thread.

By the time the PS5/XB2 comes around, theer will be a glut of storage options available. But let me just list out the three main contenders for the sake of perspective.

You can skip to the bottom of this post and just read the options if you don't wanna read too much.

1. Blu-Ray drive
   This has a read speed of 4.5MB/s. Now a 6x drive (as seen in the PS4/XB1 comes out to 27MB/s and an 8/12x drive (as would likely be in a PS5/XB1 comes up to 36 and 54MB/s respectively. 
   
   This represents headaches for game design in general and is why all games get installed onto an internal drive. Reducing the disc drive itself to nothing more than a content gate/bridge. Really, they do nothing for the console outside of just providing a cost effective way to get your games to you(assuming the prospect of going digital would be too much of a hassle).
   
   
2. SATA drive
   With this we have two options. Mechanical drives HDD (what the PS4/XB1 natively support now) and solid state drives SSD. Ideally, if the hardware is optimized for them, we are theoretically looking at speeds ranging from 150MB/s, 300MB/s and 550MB/s for sata 2 HDD, sata 3 HDD and a sata 3 SSD respectively.You can knock off 50-100MB/s on all drive types to get their real world figures.
   
   By 2019/2020.... the cost of a 1TB (1000GB) SSD would probably cost sony/ms what it cost them right now to get a 1TB HDD. And this marks the first option where a native disc drive wouldn't be built into the system.
   
   
3. NVMe Drive
   This has the smallest form factor. And is gaining popularity quickly. It uses the same base technology with SSDs (flash memory modules) but it runs a 4x PCie inteface as opposed to a SATA interface and also has a memory controller and ram cache to facilitate its blisteringly fast transfer speeds. For this we are looking at around 2500MB/s to 2800MB/s speeds.
   
   With hardware optimized for this, no game should take more than 10 seconds to load a level. And that would be even considered slow. It would also do wonders for how game engines are designed as streaming game data for vast varied worlds would become a very viable option reducing the amount of a game that  needs to sit in ssyetm ram.
   
   The costs of these drives are also dropping rapidly and by 2020 we could very well be able to have a 496GB/512GB NVMe drive for as little as it would cost to get a 1TB HDD today.

Return of the carts to home console!

I don't even have a disc drive on my new computer I built. No need for it anymore.  I could add a blu ray drive to it later but I have enough blu ray players as of now.

Maybe 100 ~ 200 GB Blu ray discs.

They could dump disks for cartridges, I'd be more than fine with that.

Do away with physical mediums? no thanks.

Option 1 for me.

*edit: crap I voted 1, thinking it was for keeping the blu-ray drive! >_> because of the order the 3 alternatives where presented in.

Thats a better alternative if readspeeds are a issue.

I think there is some confusion here.

All scenarios still support a disc. Only difference is if the console supports the disc drive internally or externally.

And even with the external options, there is one where the console comes bundled with an external drive for discs and one where it doesn't but you can buy any third party disc drive or buy an official external disc drive.

As long as they make Blue Ray movies and stuff its nice to have one device to play everything, games and movies.
Disc drives are quite cheap and they also offer backwards computability.

Also, digital only future is a future I don't want to live in for consoles so I would stop buying Consoles and just only play PC since the prices for digital items on consoles are horrendous. The main reason I have consoles is to collect a nice amount of boxes lol

So Scenario 3 because the other Scenario's will favour a lot of people going digital only.

Blu Ray Drive, or I'm not buying the console. I'll just stick with older consoles if I have to.

Cartridges? You serious, the new Zelda game is already £59.99. I'll stick to Steam.

The game would be priced $60 no matter what.  Why would Nintendo sell it for less than 60?  They always price their top tier games at 60 (Wii U and Switch generation) and hardly drop the price if ever on titles such as Smash and Kart.