I agree that it is valid for regulated intermediaries to participate. The notion of someone else holding your bitcoins, however, is anathema to the entire PKI

I agree that it is valid for regulated intermediaries to participate. The notion of someone else holding your bitcoins, however, is anathema to the entire PKI behind the protocol. Someone else has your private keys, they own your coins, period. If they happen to give you access, good for you - but don't count on that access always being there, and not going away for good because reasons. There are other services that offer m-of-n signatures so that you retain control of your keys and a service provider can still facilitate transactions. Coinbase may even offer one of these services, I don't know. But the primary service that they offer is that of a bank - a non-transparent bank that may or may not have any quantity of bitcoin at any given time. Part of bitcoin's original stated intent was to circumvent this power of banks, particularly the power to run at a fractional reserve and pull "bitcoins" out of thin air, which works fine until it doesn't. And that is exactly what Coinbase and AFAIK most of the other providers in the bitcoin sphere are doing, with many famous scams, crashes, and losses along the way.