Thats a good pt about the black hat option but I think there are two simple solutions.
1) If the original owner has not died then it reverts.
2) If the original owner has died it dissapears.
Also there are some hackables like turrets AGRS and possibly even HKs that dont go away simply because the owner died and this is where I feel making choices will be most important.
As to your first point it really doenst matter what catagory they put the equipment under your still down 1 pt. Altogether I don't think this is a huge deal, just odd.
We will always be left wanting more. To me picknig ten seems enough, sometimes I'll feel like I'm coming one short but then again so is the rest. As for the black hat, that is exactly where I last found myself wanting one more slot. But thats what makes it fun. By having that slot less we are all forced to be more creative.
Also, with more slots available, it's not only overpowered classes that becomes the problem, but variety - more classes behave and appear the same, less is unique and so on. 10 is generous I think. I can have a balanced all-rounder or a specialist in 2-3 fields!