remove the use of the older super mixins

[devoncarew]

As part of supporting the new super mixins, the runtime implementations will remove support for the older style super mixins. The dartdoc codebase is one client that uses the older style super mixins, so it should either move to the new super mixins, or move off super mixins.

@jcollins-g

[devoncarew]

https://github.com/dart-lang/dartdoc/blob/master/analysis_options.yaml#L3

[jcollins-g]

This will require some refactoring once the new mixin support is in place.