It could also be a memory limitation. It's possible for a game to have 4-channel music playing and have sound effects that temporarily cut out one of the music channels (like Aladdin). I'd say one of the reasons a lot of old games let you choose between Sound FX or Music is because they were designed for 512kb A500 systems which wouldn't have enough memory to hold all the samples for the game and the music as well.
The more colours you use in a game the more resources it needs to move everything around, so it took a pretty skilled coder to make a fast game that uses 32 colours, let alone 64. Another reason for EHB being underused is that it's very challenging for the pixel artist to come up with a 64 colour EHB palette that doesn't repeat colours everywhere. Of course they could just focus on the first 32 colours and only use the other 32 as shadow colours, like in Desert Strike, but hardly any games use the full EHB 64 colour palette for all the in-game graphics the way Fightin' Spirit does.
