Sadly, 8th gen consoles proved to the platform holders that hardware backwards compatibility is not as big of a seller anymore. Maybe the XBTwo will have BC through digital means, but I doubt the PS5 will have any at all, outside of the streaming alternative. And 3rd parties would rather make remakes/remasters at full price rather than allow people to already own them to continue playing them.
It's a shame, because for many people (especially those who didn't purchase a console the previous gen) it immediately adds a ton of value to the new hardware, offering access to a whole library of games at discounted prices, not to mention the value of preserving your collection throughout the generations.
So no, they won't stop producing PS4s for a long time, maybe they will even reach the 100$ mark. XBOnes are going to stop production earlier, though.
You know it deserves the GOTY.