Even though it makes sense for backwards compatibility to exist for the next consoles, I'll try to not get too hyped on that regard in case there is no B/C. However, shelving a feature like this would be idiotic since you want for your old library to be playable on the newer system.

But if this were to be true, I would really love not only for my PS4 games to be fully backwards compatible, but for PS3 games to also be playable through streaming.

great news!

It would be an incredibly bad business decision if they didn't have it.

BC is a must have going forward. No BC would be a deal breaker. Although very few people still play old games but at least the games they bought are still assets to them which can be used.

I think rumors like this will probably hurt them in the long run. I've seen this and stories like it popping up all over, and the general excitement I keep seeing from people who don't understand how hard this would be makes me feel like not announcing PS1-4 Bc, would be a letdown and almost free marketing for MS, if they evolved their current system into true BC.
I just don't think Sony expected it to be that big of a deal, and all they've invested in is making PS4 purchases carry over. But, the last thing they want is to have their competition branding them anti consumer right out of the gate (we've see how that works before).

Source: https://www.vgr.com/sony-has-filed-a-patent-for-backwards-compatibility/

With Mark Cerny working on this, I’m guessing that it’s going to at least be compatible with PS4, but I will be (pleasantly) surprised if it works with PS3 or older games.

THIS SO MUCH!!!

But that's not even the best collection of MGS on the PS3!

(probably not going to happen, though ...)

If PS5 will have BC then MS needs to find something else to boast about next gen hehe

In all seriousness, this is fantastic news.  Maybe we'll stop getting all those "HD remasters" that arent even that old and doesn't deserve.

What PS5 phone?

Business wise, BC, I think it would be the smart thing to do.