Is It OK?

[Mastikator]

I cannot think of a situation where a GM should overrule what a player decides. GMs should not design adventures that require players to make specific decisions.
That said, there are times when a GM could allow a player a "do-over," especially if there was forgotten information or a bad roll. Luck should be part of the game, but that has to be balanced against a fun game experience.

Hard disagree. I can and will deny certain player decisions in my games, like racial depending on campaign. Like character traits depending on theme. No anti-adventuring cowards in my heroic fantasy thank you very much (nor do I take kindly to PVPing or murderhoboing- if that's what your character would do make a new character).

To @OP, I have never run a game where cowardice is anything but a big flaw, and if cowardice translates into "yeah I'm not going into that dungeon", or "I'm not rescuing the villagers from the ogres", then you either make a new character that will go on the adventure the whole table signed up for. Or find a new table where that is OK.
I can't speak for other DMs though. And if cowardice is something you intend for your character to overcome then it's a fine and good flaw.