I'll preface this by saying that I think Sony closing down the PS3/Vita/etc. webstore sucks, and represents the beginning of the end for not only those platforms but the library of PS1, PS2 and PSP classics that will also soon have no place to call home. (Some PS2 classics run on PS4, but the library of PS2 classics on PS3 and PS2 ports on PS4 are mutually exclusive as far as I know.)
I kind of get why Sony's doing this. it definitely doesn't do much for their bottom line, and yeah I guess don't rely on Sony to keep these things alive for us blah blah blah. But that means the people who do care are caught in that terrible valley between "financially lucrative enough to put energy into selling" and "financially dead enough to give away for free." There's clearly some value in continuing to provide access to and sell PS3, Vita, etc. games, but no value to Sony in trying to either update that infrastructure to work with the modern systems they're setting up for PS5, or making that infrastructure work with the legacy games in such a way that allows them to remain active on the webstore.
But Microsoft has a similar problem: 360 games are stuck on an older webstore separate from the Xbox One webstore. They didn't close down the 360 webstore, and at this point it's pretty obvious either Microsoft's going to leave it in place or put in the work to migrate everything over, because it would be ridiculous to make backwards compatibility such a big part of your pitch for the next generation of Xboxes and then remove a key method of buying those games. Sony has made a decision to actively decommission their infrastructure. And you can say they've got good reasons for doing so--they want to concentrate on PS5, the old infrastructure is shit (I don't know but I've seen that cited as a common reason), nobody's buying those games anymore anyways, etc. But they still made the decision, and I still get to be unhappy with it.
Long story short, I've been busy trying to dump my PS3 games in preparation for an eventual PSN shutdown on PS3, and doing the same for Vita as well. Because we are very close to seeing what happens when your digital library is made obsolete because no active platform supports it anymore, with the PSP. Will they shut down the download list functionality on the PSP after they sunset PSN access on the Vita and PS3, which are the only two methods of buying PSP games now? And obviously, what happens to Vita and PS3 at that point? Storing a big library of PSP games isn't so bad, but PS3 and Vita games are quite a bit larger and in the case of the Vita, your options for storage are extremely limited.
I don't think they "don't care". It's more like: Sony focuses on other stuff than BC for pre-current gen consoles. Stuff they deem far more important than that.
Offering PS5 exclusives right off the bat might be an example. And if the current hype level around PS5 is any indication, they probably bet on the right horse.
I mean, this is functionally equivalent to "they don't care."
