This isn't true backwards compatibility as you can't play the old games you already own. It's just whatever games are part of the current PS Now subscription and a few more
All PSNow games
I see this more like a Netflix where you have access to loads of games, not all of them you'll like and then maybe you get access to the big studio games a year or so after release. So it could be a case for some people that it's worth signing up for a month at a time to play through some big games they haven't bought.
I still have my PS3 slim and PS2 slim hooked up to the TV in my study and I rarely play them. This is the reason Sony isn't investing heavily in backwards compatibility. It's a topic that people love to harp on about and it's a nice thing to have but the people who would frequently avail of the feature are the minority. If the classics on the Playstation store were big sellers during the PS3 or PS4 generation then Sony would invest, they obviously haven't been. That's my opinion on the whole thing anyway.