The following GitHub issue tracks that feature request. It might be cool to ship a default classification list for common banking and shopping sites so they are already "contained".
Not the PM you're looking for, but: that feedback has definitely already been recorded.
1. Hello potch!
2. Yes, this is among the most requested features we've seen so far. Containers in Test Pilot will remain in active development for the foreseeable future, so I wouldn't be surprised to see such a feature forthcoming.
If a FF PM is reading this: being able to register a domain for a container type would be a killer feature.