Aside from game design, I can't figure out why there should be two clicks to repair and install something. Is there a benefit to carrying broken modules that I'm not aware of?

Seems like it would be smoother to have something install when you repair it. Would certainly cut down on all the unnecessary page scrolling.

Am I missing something?

I often repair when a module breaks on uninstallation, when I specifically would not want to reinstall it.

Would it make a big difference if you couldn't? I don't understand the advantage aside from preference. Myself, it sits there broken until I need it, but I don't know if one of our ways is an actual advantage to the other.

Broken modules do not add to your upkeep. Mods that are uninstalled but still viable DO require upkeep.

That was my thought too. I hope it's right, but that's why I don't repair until I need them. In that case, clicking once to repair and install makes sense.

I'll have to keep an eye on that - if this is true, then I've been wasting money. And yes, if this is true, I've been doing it wrong, and the suggestion to combine the repair and install actions makes a lot of sense.

Exotic Pulsers and Ion Ballistaes is why mods should not automatically re-install upon repair
Every time I rank up I uninstall these mods(as should everyone) if you repair your mods right away without taking any other action you get a 10% discount on the repair so it would cost me more credits or I would have to uninstall these mods twice.
This also would apply to the Encephalon or Drannik Cores which I only use when I rank up.
Also I swap different mods in and out depending on what I am currently trying to achieve.
Having mods auto-install upon repair would be costly and inconvenient.