I suppose not inherently, but it is not only rather against the philosophy of BTC and many of those who hold it, who would therefore probably never adopt such a system, but it is also against the current characteristics of the currency, which might make it very difficult suddenly to acquire BTC if there were a sudden demand.

So I'd say yes, it is incompatible with BTC and can be expected to be so for at least the short and mid-term future, and perhaps for the rest of its existence.

I would never keep BTC with an entity that did not have access to its full complement of deposited BTC, though I would prefer some large percentage of that store of BTC be kept in cold storage of some kind in case of hacks, even if that sometimes led to inconvenience.

Actually, I generally would not keep BTC with any entity other than myself for any length of time, if I could avoid it.