Can somebody explain what impact integrity has on the ship? I just got back from month-long exploration, and there's plenty of others that have been out there longer, and I'm sure are at 0% integrity. The ship still seems to work fine (as long as we don't face-plant into a neutron or black hole). The "repair all" fixes the hull and module strength to 100%, and that's cheap.
If the ship started frakking up at 20% integrity, or hull-breach at zero and then explode, I think I'd be concerned with it. But so far, other than the regular station repairs, I don't think I've ever clicked specifically on the integrity option and repaired.
Honest question - does it matter?