The whole amud talks about how Dovid was a chassid by going above and beyond to reduce his kavod and not be like other kings who are always seeking kavod.

Isn't there a concept that a king is not allowed to be mochel on his kavod?

He's not allowed to be mochel for a bizayon, but he doesn't have to seek extra honor for himself either. The Gemara in berachos was talking about things like his learning schedule - it was not a bizayon, just that he could have gotten "more" kavod.

In particular, it was discussing his bloodying his hands to be mattir a woman to her husband and asking Mfiboshes to verify. This is not a bizayon persay; it just wasnt very respectable.