I've wondered about this quite a bit, since I run computationally intensive analysis on sensitive data, and some of the same thinking would apply in this context.

In brief, I could provide an appliance on something as trivial as a Raspi that updates itself over VPN, and would let you run the services on your own systems. Would that work for you if one of these providers did the same?

Obviously we could do better with a custom system deployed onsite, but the idea is to simplify the process and potentially eliminate cost of getting started; similar to Square sending out card readers.