Any quarter decent imgui implementation will idle when there's no input or active animations, and the renderer can generate dirty tiles or rects to unnecessary redrawing -- if it matters, gpus are ridiculously overpowered for drawing a bunch of rectangles. Ui logic is usually firmly in the microseconds realm.
I really wish this were built into imgui as a first-class use case instead of requiring a hodgepodge mix of unofficial hacks.
I recall the author posting an imgui update saying this will be an officially supported mode, but AFAIK it's still not the case. Otherwise I would be building all my applications with imgui going forward.
Re-rendering the screen, even if it's fast, incurs a lot of memory bandwidth to draw everything and swap framebuffers etc. Not something you'd like to happen on mobile, in particular. Just because the waste is "small", doesn't mean it's acceptable.
I agree that this is not a necessary downside to immediate mode GUIs, but we're talking about egui specifically here. AFAIK, egui always redraws at some relatively high rate even when nothing is happening. (I'm having trouble finding documentation about what that rate is though.)