Our conclusion was that the only way to get the required level of management per tenant, and to support truly massive number of tenants, was to use an inprocess database over https ie SQLite and Apache. But, SQLite has an image problem, it's everywhere, and nowhere. It's built with some fundamentally different decisions than other databases, and isn't traditionally used for web applications.
So that's the course we took, links in my profile for more info.
Why not, but you introduced a whole bunch of new issues. SQLite only supports a single writer at a time. This is a problem if you have a lot of users on the same tenant. This is also a problem when you need to create an index, for example, which is not a background operation.