I like the general idea, I'd just set it up a bit differently: Allow cruisers and above to equip a "escort tether" hullmod. That would grant them a slot in which a frigate could be put, erasing it from the normal fleet menu. That frigate then deploys automatically with the capital ship (without costing DP) and is on permanent escort duty. It is also automatically (i.e. for free) repaired and maintained by its mothership in between combat.
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I feel that is better handled by heavier fighter LPCs. Fighters are already coded as tethered escorts on permanent escort duty. As it is right now, I feel a LPC frigate would run into weird coding issues. Like crew/cargo losses. Is it fully automated now and doesn't cost any crew? In terms of deployment, not all frigates are equal. Would there be a DP cost (or an OP cost) difference when you use a Shepard vs a Hyperion in this slot? Can the player take direct control over this escort frigate (negating the effective escort requirement) or is it more like a fighter?
I'll just chip in and agree that with the opinion that: Any out-of-combat logistical changes will be exceedingly unlikely to change the desirability of frigates in combat. If you want frigates to be more desirable to use and replace in combat, they need some bonus rather than simply being cheaper outside of combat.
I think there's only so many knobs you can turn in combat. Any fundamental changes to frigates affects the entire game, not just end game fights involving battleships.
I see it this way, the knobs you have to turn are:
1) Offense (How quickly you send the enemy HP to zero)
2) Defense (How you keep your HP above zero)
3) And stuff that affects the other two indirectly, such as Movement and CR
Frigates already have their movement knob turned higher than other ship classes, so that is not much help (and the higher you turn that, the more twitch reflex reliant the game becomes - also you start running into AI perfectly dodging all your shots if you tune it really high).
So lets talk a look at defense. In order to have a noticeable effect, we will have to turn knobs 1 and 2 by factors of 100%, not by 10%. We already have that kind of variation (i.e. 10-50%) within the frigate class, and I think people are still complaining about the entire class of ships. Doesn't matter how you get that 100% more durability (base flux, armor, hit point stats, some kind of 50% evasion, a global 50% damage resistance, etc), as in the end its all trying to just make them more durable.
If a Battleship destroys a frigate in say, 4 seconds, no one is going to notice a 0.4 second difference. They might notice a 4 second difference (i.e. 8 second total) though. However, that would throw off the early game a lot, increasing frigate vs frigate fight times by a factor of 2 (or more than 2, given the way shields and flux work when you back off). In turn would also require a CR increase, probably a factor of 2-ish. Would people be happy with factors of 2 or more change in the early game combat time?
Note that kind of durability is on par with destroyers. It also means, two frigates should handily beat a destroyer (approximately equal damage output, higher speed, and twice the toughness). Unless you also change destroyer defensive stats.
Each class of ship is roughly a factor of 2 in durability higher than the previous. i.e. a Medusa has twice the shield capacity of a wolf, the Aurora has twice the capacity of a Medusa, and a Paragon has twice the capacity of an Aurora. Hitpoints scale roughly that way as well, but armor interacts non-linearly. So a typical frigate is like 1/16th of a battleship. Changing that dynamic without also changing other ships along that chain I think will have unintended consequences.
On the bright side, this is easy enough for anyone to test with a mod. Simplest thing to do is take the base spreadsheet and simply double the defensive numbers of all the frigates in the base game, see what happens, and come back and report.