Before discussing the merits of the system, it probably should be outlined in more detail...
First, let's determine the actual rank of your "captains". In order to do this, I think it's important to equate hull sizes in GC3 with typical ship classifications in current navies. While it appears to be about ship size, it really is more about crew size since that is what determines the managerial and logistical needs of the ship's CO...
Huge ships, being the largest, would correspond to the largest battleships and carriers we have ever had, what we might call "Super Battleships" or "Super Carriers"...the CO,
, and several other people (CAG, department heads, etc) would all be captains, and the CO in particular would be a very senior captain...
Large ships would correspond to battleships, battlecruisers, and fleet carriers...like the huge ship, the CO,
, and possibly several other people would all be captains, with the CO being a very senior captain...
Medium ships would correspond to cruisers and possibly other vessels like escort carriers or amphibious assault vessels...these ships are going to have a captain as a CO and probably a commander as
...
Small ships would correspond to destroyers or frigates....these ships would likely have a commander as the CO...
Tiny ships would correspond to a variety of smaller vessels like patrol boats...the CO could be a Lt. commander or a very senior/experienced lieutenant...
To simplify:
Huge (Super BB, Super CV) - Captain (one among many)
Large (BB, BC, CV) - Captain (one among several)
Medium (CA, CL, CVE) - Captain (probably only one)
Small (DD, etc) - Commander
Tiny (Patrol boats, etc) - Lt. Commander or senior Lt.
The way I see it, I wouldn't even bother with the CO of small or tiny ships as that would get rather tedious...worrying about the CO for medium vessels would be fine in the mid game but could get tedious late game....might be better to have "captains" that represent particularly gifted/experienced officers that can be added to medium, large, or huge ships to provide bonuses, but aren't required to field those ships...
Now, let's look at your "commanders". Personally, I wouldn't get too attached to the American ranks of lower and upper rear admiral. Probably best to have three generic ranks for flag officers: Commodore, Admiral, and Fleet Admiral. It's simple and doesn't get too bogged down in the specifics of USN commands. One could argue that it might just be best to have "admirals" and focus on gaining experience/traits rather than a rank, but to each their own....