Ran into a problem in #1898054: Convert comment module to Twig where the testbot was failing because Bartik didn't have it's templates converted to twig files - see comment 4.
This alerted me to the fact that tests against themeable elements that Bartik is overriding are being run against Bartik, not against core.
Since essentially zero themes are using Bartik as a base theme, we really want our tests to be run against the core template files. It would be very easy for somebody to make a bad change to a core template file, forget to update Bartik to reflect the change and see tests passing that should actually fail.