Is there any disadvantage to promoting early?

Solution 1:

During the main game, promoting your units may be better since it would require less re-leveling, as they retain their level (instead of having it reset to 1). Reincarnation is better overall, but costs more mana, so it really isn't worth it until post-main-game.

This post may explain it a little better:

You get to keep your levels as-is, almost as if that character had been of that tier all along. In addition, full reincarnation costs cumulative amounts of mana (more each time) and the rest of your mana is basically wasted. Promotion costs mana, but doesn't discard any additional mana you have.

It also doesn't slightly decrease the levels of your skills, which frequent reincarnating does.

To summarize, no, promoting does not have any real disadvantages. It is advantageous during the main game before you are attempting the Carnage Dimension or Ba'al.