This could be interesting, if there was a level of Structural Integrity you started out with, that could never be returned. It could be added as an additional item, sort of like an armor, or could be a cap to your max HP, that gradually goes down. I.e., the more damage to your SIF, the less total HP you can have.
Ideally, in the OP's example, the SIF would also be added with a much more robust systems damage mechanic. Every system, like the deflectors, or the engines, or the warp core, would have a damage amount. The total HP would become Structural Integrity, and as long as there was a little bit of that left, even if all the other systems read 0%, you could hang on and get a little bit done.
Of course, that requires a pretty big overhaul, so I say we stick to simplicity. Add a SIF, and the weaker it is, the further from 100% your total HP can be. Cap it at a 0% SIF means 50% HP max, and we've got something interesting. There will still be "bouncing" healing, but at least it'll go from 5-50%, rather than 5-100%.
The new party line is: in the 30 years since the tv shows and movies ended, force field tech has improved. Examples of this are all things photonic and structural integrity field. Hull stat actually represents various fields more than physical structure.
Since STO ships are powered by anti-matter, I would add the containment field to the list of pretty important stuff that hull represents. That gets taken down and there are a lot of letters to families to write.
The vast amount of damage that these fields can handle makes the capacity of the physical structure of little account?
All abilities that raise the hull actually aid in stabilizing these fields or rebuilding them.
These assumptions explain current game mechanics perfectly. It also explains why unlike in the tv shows and movies, we never see parts blown off of ships. Once the fields are totally disrupted, which takes a staggering amount of punishment compared to previous eras, the whole ship just goes boom. It also helps explain the enormous change in success against the Borg. I guess that it also handles the personal shields and armor used on the ground as well.
Wow. Nicely done. Answers many questions and concerns. I think you should repost this in general feedback.