I keep all my consoles (because I'm not a weirdo) so it wouldn't matter to me at all.
Unless your console dies, consoles are not built like the NES any more, if you think your PS3/4 or 360/XB1 is going to work in 10 years time, you might end up disappointed
I don't
need BC, but I'd be thrilled if we get it. It's one less box under the TV, one less set of wires, a few less controllers lying around, less things to dust
One of the best things about PC is you can buy a decent PC then have access to games from the last 30 years. Why wouldn't you want a PS5 that has a PSN stocked full of PS1/2/3/4 games?
A PS5 that has all your old games from past systems ready to re-download (if you went digital) or that are just a disc away from you enjoying again?
Like others have said it's a good way to lock someone into the ecosystem. If the architecture is similar and it's not a huge pain to make them BC, then it seems like it would be the smart thing to do. When most people have phones and PC's capable of playing games, and the games they brought on their old PC's and phones, why would you buy a console with only 10 or 12 rushed out the door launch titles?
Nintendo will be an interesting case, as if the NX doesn't have a second screen it will make BC for Wii U games a challenge