Aka, the "second-hand smoke" effect of gmail (or any similar service). Even if
you are fine with giving your data Goggle (or Facebook, etc), it's a problem if your forcing that decision on others.
The solution is probably using email in a manner closer to how it was originally designed: many local MTAs instead of a handful of centralized MTAs.
Here's a product idea, which could make someone a lot if they can find a way to implement it: a home server that is a minimal, secure, locally contained, turn-key home email MTA (with some localhost-only IMAP/webmail interface). You sell the server (and maybe a 1-time service to help people set it up).
This server would have to include a "choose your vendor, enter your credit card, click subscribe" super-easy interface to let people subscribe to vendors (multiple, if desired) that provide lower-MX-priority backup MTA services. (perhaps with an optional "hidden MTA" option, where your home server and lowest MX is only visible to the service, so the home router only connects to know hosts, IFF that is something that the customer wants.
People already understand local-only delivery because it emulates snail-mail. If you can let people receive messages and data unattended and asynchronous, so they can run the server when they want and receive their data directly (nobody else involved except for the backup services of their choice, then you have a product that will sell. It doesn't even need to have to have great uptime (that's what multiple MX records are for) or performance.