Add missions to destroy turrets and various FC damage to disable all kinds of services.
The owner of the FC can always dock with his own FC and repair it.
(if I'm not mistaken, you can do it remotely through the FC menu.)
Having spent more credits on repairs.
If the FC is in a safe system and you are loyal to the fraction in the system then you will get more protection ships flying around and it is difficult to damage the FC.
Bad idea IMO. The people who just want to see the world burn would be able to indefinitely keep your FC damaged and you would be 100% grounded as a 5 billion Cr FC owner. They could do it in Solo, which effectively renders ANY counteraction impossible. (Unlike the BGS for example, where you can counter with BGS activity). Unless they could never damage the drive? So you can jump away and escape (but then they can just follow you so...).
No, definitely a bad idea for the game. It would only lead to more division, salt and toxicity in the community.
To be constructive: I would rather they enhanced the megaship missions. Steal specific cargo from its cargo hold for example.
::EDIT::
Your example of burning stations isn't the greatest one. Have you seen how many are still damaged an nobody cares (apart from OpIDA). Besides, if in addition to Tritium hauling you want me to haul bazillion of materials to fix my carrier, because you fancied damaging it 100000 times in a row, I think I'll pass.
I've organised the event to fix Obsidian Orbital when it was damaged. NEVER AGAIN, worst grind ever.