More “input lag”, picture quality takes a hit, they’re more expensive, and the circuit boards are more prone to failure and more expensive to repair/replace when they do.
Sources are Amazon, Google, and common sense.
Btw, in terms of input sources, different resolution doesn’t mean anything. The vast majority of TVs use the same input board and picture processing for HDMI and component input. Even if the Wii only runs at 480i, if the TV truely is the problem it’ll also have the “input lag” because it’s signal will be going through the same board, same chips, same post-processing as the PS3 on HDMI.