Eh... I don't think so really.
Depends on their objective. A PS5 sale is more valuable to them than a PS4 sale, because the PS5 owner will probably generate more revenue for them in the long run. Selling more systems isn't necessarily their goal. And even at 200/250 I don't see the PS4 being a very attractive proposition because of the 300 dollar XBox Series S and Swtich.
The PS2 had a lot of success post PS3 but that was a different market, and Sony was launching the PS3 at a very high price to the point where a cheap PS2 wasn't going to influence it. I can see Sony just letting hardware sales drop quickly.
It's not a point of selling the PS5 is better, nobody will have any reason to buy the PS4 Pro at all, they are literally killing their own product.
I know they want people to move gens, but for people that are waiting for a cheaper system to get into the current to be old gen... they just won't have any option.
Better phase it out than to let it be priced the same as the next gen version of it.