Thing is, you keep emphasizing that a few beam turrets on the carrier will let it fight. But it will NOT save its sorry butt. If the carrier really gets ambushed, with or without beams, it is going DOWN. There is no way a hybrid ship can stand up to heavily armored hard hitting destroyers.
True, if a beam-heavy destroyer jumps in on a hybrid carrier-battleship, without the support of its air group or escort, it won't put up much of a fight. However, the presence of anti-warship beams on the hybrid ship forces the enemy to deploy a destroyer, instead of something smaller, cheaper, and more readily available. If your eggshell carrier gets separated from its escort, it's going to have a hard time fending off a cruiser with its point defenses, and it's just meat to a corvette.
Specialization has its merits, but you can only take it so far. Once your enemy identifies the weakness of your vessel, they will adopt tactics to exploit that weakness. If you over-specialize, your weakness becomes easier to exploit. A Hecate is vulnerable to other large warships, in the absence of escorting vessels. Your eggshell would be vulnerable to
any warship without its escort and could potentially be kept so far from the battlefield by the mere threat of counterattack as to render it insignificant. The Hecate might not be able to wade into the thick of battle, but if pressed, it can hang with another warship long enough to deploy additional wings and regain the advantage. Take away the beams and armor, and it has to run, leaving any wings already deployed to fend for themselves.
Before you parrot your own line about a heavy escort solving everything, bear a couple things in mind:
1) Reliance on a heavy escort is a weakness that can be easily exploited. Lure the escort off in one direction, while launching the main attack from another.
2) A heavy escort is not an impenetrable shield. One can shoot around an escort ship, and it doesn't have to stand against the escort's fire very long, if you've stripped the armor off your carrier.
3) In the FreeSpace universe, situations often arise where it is impossible to deploy heavy escort for a ship that needs it.