I guess I only care that I can do it at my broker, now that you ask I would be surprised if there are any brokers who wouldn't let you do it. It's a common strategy for exactly that reason and some entities are required by their bylaws to either do that or have insurance coverage that would actually cover 100% of their loss which as you all did a good job of pointing out none of the current products do given the aggregate loss limit.
I am not the best person to answer this since I don't do major in shorting. Since I have PM with IB I have been using them as me go to for shorting these days. Never noticed a wide disparity between brokers with the borrow rates.
Can be a significant disparity in short rebate rates depending a lot as to if the position is in their "box" or do they have to do a locate. You can see the "market" rate by backsolving the option parity equation - but parity could be a band if it's HTB, but you'd still have a sense. Some slightly better rates if the custodian has an ongoing relationship with you. If Schwab/TD becomes a reality they are going to have a "size" box for lending.
Just pick any two brokers that are "too big to fail" and you should be diversified enough at any net worth level. However, they do treat you a little different when your account exceeds $1M, give you a special # to call when you need help even when you are self directed.