Considering that I have worn out at least one belt sander and wouldn't even consider a shop without one I think you are completely out to lunch.
That said, what the OP needs is to be able to true up his panels, I assume some that are already glued up, otherwise he is better off to try to improve the alignment on future panels to eliminate the need for either sanding *or* planing. Cauls are the obvious (to me) answer for future panels. For truing existing ones the belt sander works well, the main problem is that they are very aggressive. I have overcome that in part by using finer grits than seem reasonable. For a glued-up furniture type panel I wouldn't use anything coarser than
150. It works slower and doesn't create the problems you get with coarse grits. Might even go a lot finer than that.If you want to plane, fine. It will probably give you a better surface than sanding once you master planing. I haven't and probably won't ever get real good at it because I don't have the time to spend in the shop. I don't care what the experts say, it is a challenge to learn how to do a good job with a hand plane.
Tim Douglass