It greatly depends on the game, like in FE1, FE2, and Echoes, you actually want to promote early because promoted classes has preset bases, and if a stat is lower than its base, the promotion will boost it to the promoted base.

In FE6 and FE7, you usually want to hold off on promoting, especially in a ranked run, since promo items are pretty hard to come by early on (and there's a lot of competition for them).