If we are taking into account basic attacker hulls, then yes, I wouldn't equip it there, unless you are Vaulter or Nakalim with 3 support slots. But Protectors have 2 to 4 support slots, so it have its use. Systems repair your ships by 10% each turn, so just one repair module speeds up repairs by 1.5 times, or allows repairs out of your territory at 0.5x rate.

If repairs as machanic early on is even valuable is a different debate. I'd rather see static HP repair values, rather then percentages.

It's not something you use in the earlygame. You use it to make fleets that can't be worn down by trash spam in the mid to lategame. If you spread half a dozen of them across a full fleet using upgraded protectors/coordinators and upgraded hunters or early carriers, that's a fleet that cannot be killed by anything other than a similar overwhelming concentration of force, strategics, and advanced technology in a single fleet -- or a Juggernaught's Ion Wave. And with the Full Reserves tactics card, that fleet can kill an infinite number of lesser fleets in a single turn.

Depending on your fleet's composition and where they are in a Floatilla(not to mention what you equip on each ship class), Nano Bots can have an impact in keeping your fleet at full HP without using battle tactics to keep them there. More effective in Single player games since the AI rarely has ships that do signficant enough damage that overwhelms the repair bots but in Multiplayer games, Nano-Bots lose their effectiveness since more often than not your ships are badly wounded or destroyed outright by ships of equal caliber or stronger. Therefore you're better off loading Floatilla Shields, Evasion Modules(if those are even worth it....), Boarding Pod protection(Kinetic slugs help but extra protection never hurts) and Manpower/Siege Modules for invasions.

A better question would be whether Fighter/Bomber and supporting modules are even worth it.

There are always "better questions", so thankfully there is no limit to the questions we can ask or threads we can make :)