I sometimes use regeneration, primarily either for advanced ships or my Star Whale vessels in one of the settings, where I wanted them to feel organic. However, it uses up space I could use for laser lances...:)

I use it on B5 ships to represent Self Repair that is present on various Ancient vessels and the White Star.

Yah, regen only repairs hull.  We weren't playing with Damage Control, though, and by the time he went "Uhh...  can we use damage control?" a number of my vessels would've needed to have used it on previous turns, and we didn't want to retcon.  We're bad at toggling options that need to be in effect from the beginning of the game, and we generally don't use damage control because it's kind of annoying / random enough that it can be either really useless or really frustrating.  I guess we'd rather see Damage Control as a starship trait than having it be a universal combat option.  Might have to hack that together...

But yeah, regen without Damage Control seems rather weak; it may keep you alive, but you'll be out of systems unless all that hull damage came from something like EHD or Cata, or any other effect that inflicts many hull hits without the corresponding number of systems hits (normally 2 systems hits per hull hit on average; with EHD, expectation is 2/3 of a system hit per hull hit, and with Cata it's 4/7 of a system hit per hull hit).  So it's a specialized counter-trait for those kinds of damage sources and not generally worth using otherwise without Damage Control.  I ended up using Directed Fire to cripple his engines and weapons rather than going for hull because I simply didn't have the firepower to destroy it outright, but I could definitely render it useless.

We hella banned it because it breaks campaign systems.