I wouldn't stress too much. I don't know if I sang much when I was 2, but apparently I didn't talk much, so I'd be surprised if I sang - and I'm alright at it now.

Can bub mimic you? My bub will mimic me doing arpeggio sounding stuff - if he's in the mood and not too tired and he can't see his blocks, trains, the tv or any food.
It's definitely not a priority for him, to be able to sing, so he doesn't spend much time on it.

I guess just keep singing fun, so that he's interested in joining in, and the more he has an opportunity to sing, the better he'll get?