No, PS4 games are not developed around a SSD, you can just some load speeds and that's it.
The SSD of next gen is a vital part of game development from now on, last gen simply can't compete with it just having a SSD on it (which you can try on your PS4 and see how it works).
An SSD on a PS4 doesn't make much difference because it's SATA II as far as I know. Pro has SATA III and can make a fairly significant difference when it comes to things like load times or pop in. I know an SSD in Pro wouldn't make it like a PS5.
You wouldn't market Pro as next gen, but you would market the SNY brand and specs against XBSS.
8 Cores vs 8 Cores.
4.2 TF vs 4.0 TF.
1TB SSD vs 512GB SSD.
Pro even has 9GB RAM total vs XBSS 10GB RAM.
I think it could work if SNY planned to keep selling a version of the PS4 if not both. They could still keep PS4 and have it at $199 in this scenario.