> People would gain power just by being popular.

This problem already exists. Liquid democracy does not eliminate it, but it should lessen it for a couple of reasons, but probably most importantly because it gives people continuous control over their delegation decision. Right now the election cycles themselves exert tremendous undue influence over political outcomes, an implementation side-effect that is not an inherent property of democracy or particularly reflective of the popular will. Liquid democracy ameliorates this side-effect.

For that reason alone, it is worth serious consideration.