Throughout gaming history, hardware has sometimes had pro/refresh versions with notably different specs.

DSi

New Nintendo 3DS/2DS

PS4 Pro

Xbox One X

PS5 Pro

And then there are other situations like Game Boy Color that had hundreds of its own games and a generational leap in graphics but is considered a refresh by some. But that's not the focus of this thread.

DSi and New 3DS/2DS had some physical games and plenty of digital ones that were incompatible with their base counterparts. 

When we go to home consoles, there is nothing. Anything that plays PS4 Pro, Xbox One X, and PS5 Pro can play on the base counterparts. Even Cyberpunk 2077 still plays on a base PS4. However, it warns you that playing on PS4 Pro or higher is recommended. 

Would it make any financial sense to have released titles compatible with PS4 Pro, Xbox One X, and PS5 Pro that can't be played on the base hardware? 

Never

Sony hasn't exactly released a lot of first party games these past few years, do you want no new games for the base PS5?

Given that the mid-generation refreshes represented a fraction of the overall sales of each generation, no. Any game that was made only for the mid-gen refresh would be dealing with a much smaller user base. The lone exception to this might be the Game Boy Color, whose sales were fueled in part by something the PS4P, X1S, and PS5P didn't have, which was Pokemon.

How about going back in time a bit more. Megadrive/Genesis and 32X ring any bells? Even the Sega CD/ Mega CD could count, as it added a faster CPU and enhanced  graphical capabilities.

However, I'm pretty sure the flop of the 32X is also the main reason why home consoles don't lock games to an hardware upgrade, considering how bad it sold. And with modern 3D technologies, it's useless anyway as a "Pro" console just runs the games of the main console better in several potential ways, like higher and more stable frame rates, better graphics, higher resolutions...

Long story short, nope , that's a very bad idea, both in practical and in business sense.

Absolutely not.

BraLoD is right, splitting the market this far through is just bad roi .

No.

I hated when Nintendo did that with the 3DS.

If they do, they're effectively a new generation and should be named as such. That said, at the moment I'm not against more frequent and smaller generational leaps that have stronger guarantees of backwards compatibility. If you do that, you should also call it that though.

There's various issues with the idea of developers taking advantage of Pro consoles to that degree. One is the way a Pro console works nowadays is the GPU is improved a lot but that's basically it with the CPU being just about the same and games nowadays scale massively in terms of graphics so if games like GTA 6 are gonna run on the Series S then unless it's something that is using path tracing as a requirement I dunno what game would run on the PS5 Pro but not the base PS5 this decade even with the settings turned down. The New 3DS was different in that it had a notably better CPU which I imagine contributed to it getting a handful of exclusives but even then it wasn't that many at all cause the far smaller install base makes it not worth it.

The biggest issue is how long big games take to make nowadays. A game so graphically demanding that the base PS5 couldn't run it at all that isn't just a basic tech demo would take so long to make that assuming development started last year we probably wouldn't see it till the early 2030's at which point the PS6 will have been out for years so they may as well have just been targeting that level of hardware from the start if they wanted to push graphics that hard. Now this is all moot cause unless they changed policy Sony won't allow PS5 Pro exclusives but for the reasons I mentioned that policy being in place doesn't really matter at all.