It would be somewhat disappointing, but not the end of the world for me in regards to picking up the Switch successor. In the end, if the new games are good, that’s all it’s gonna matter. The Wii U had BC, but if that’s one of the big things it’ll be fondly remembered for, then it means it had more problems overall which led to its abysmal sales performance. I still have my GameCube even though I have a Wii. Same with a GBA even though I have a DS lite.
With all that said, I think the successor will have BC. Nintendo is aware of the Switch’s incredible library of games and how they need to handle the transition to its successor.