Just curious. Does anything bad happen if I just leave the offshoots to do their thing? They come up pretty frequently. Thanks.
Sometimes offshoots are called "suckers", because they could theoretically suck some of the strength away from the main plant. They are also pruned sometimes for appearance, to maintain a tree-like form instead of allowing it to get bushy. But with both your plants I don't really see that as too much of a worry at all, it's just about your visual preference. If you don't want the bushier form, I would still let them grow a bit then separate and repot, since I'm sure they're both desirable plants for trade in your area. :)
Yes whilst curry leaf plants can be propagated from runners, cuttings and seeds, for banana the offshoots is the only way to propagating the plant.