If Sony isn't on the BC train that Microsoft started (which I'm happy they did) then PS5 will take a big backseat to the next Xbox console
the BC myth has never shown success. ever
a) early adopters (the ones who sell out the new systems) don't care about BC. They literally want every new shiny game.
b) by the time those who are most likely to consider BC in their purchase decision are ready to buy (at a lower price), there are enough current gen games on the market for them to no longer care about BC.
If you look at BC through the ages..
2600->5200 - didn't help in the slightest
SMS->MD - peripheral solution. largely ignored
fast forward ELEVEN YEARS
PS1->PS2 - hard to say, though there was a clear explosion in sales with GTA3.. so it is easy to say that BC didn't account for why PS2 was so successful
GCN->Wii - I mean... it's barely worth discussing. GCN install base was tiny by comparison, and the big driver was Wii Sports
PS2->PS3 - PS2 games don't seem to have helped the lowered sales of PS3 from the previous gen.
XBOX->360 - BC support was terrible and limited. Clearly not behind the console's success.
Now there could possibly be a correlation in the handheld market.. but as that's an entirely different market with different purchase patterns.. not sure there is validity in talking about it here.
if EITHER console does BC next gen... it will be because it was probably easier to do it than not (something very possible if they continue sticking with x86-64 hardware..). If they switch hardware (ARM), I can almost promise you that the only BC you'll see is streaming.