As someone who is financially... uh... let's say limited, backwards compatibility would actually make it a lot more likely that I pick up a new console sooner rather than later.
I never am able to play every game I wanted to from the previous generation by the time a new generation roles around. Hell I still have a bunch of GCN/XBOX/PS2 games I intend to get to someday, not to mention some N64/PSN, and SNES/GEN (that's about as far back as I'm willing to go). If a new console could play the games from the previous generation I'm still interested in playing and opens up a whole suite of new games to me, and also I factor in that this means I could trade in my old console a brand new console purchase which is probably the most important part, the idea suddenly seems much more reasonable than throwing hundreds of dollars on a brand new console that hasn't yet built up a huge library of games I want would otherwise be.
So if, for example, I could play Wii U games on a Switch and that freed me up to trade in my Wii U towards that Switch I could probably talk myself into doing so, if not right now then almost certainly when the new Mario game comes around. But since I can't, I probably won't get a Switch for quite some time, possibly years, unless somehow my financial situation changes for the better.