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It depends a lot on what rôles the sugar serves other than sweetening.

In cake recipes which "cream" sugar and butter, the sugar has a mechanical rôle. The sharp edges of the crystals cut holes in the butter, softening it. If your frozen banana is frozen enough to have small ice crystals you might be able to reproduce the effect, but it's not easy.

In other recipes the sugar is structural. E.g. in flapjacks, the sugar binds the oats together. I actually use a flapjack recipe without the sugar to make roasted oats for my breakfast, but in that context I don't care that it falls apart. Using banana or stewed apple probably wouldn't work because there's no water in the recipe; at the very least it would be necessary to add some flour or cornflour to compensate for the extra water.

TL;DR: there's no "one size fits all" substitute for sugar.