Lots of people are drawing from the contemporary USN, but I think a better idea might be to look at the RN. The key here is that in the Royal Navy, commodore is not traditionally a flag rank even though it's equivalent in grade to a one-star rear admiral. You see it in the army, too, where the UK brigadier is an 0-6 field-grade officer, not a general officer.
If you look at it historically, commodore is the highest rank that could command a ship. Flag officers always worked through a captain, while commodores would sometimes command both their own ship and the squadron.
So yes, a commodore makes complete sense as the commanding officer of a starship, while none of the admiral ranks do.