I've broken this out from #1593454 as separate feature request ticket.
As a side note, the preconfigured browser instance (the "Open Browser" functionality) can't be started with a specific profile. You can specify a path to a different Chromium browser, but it will always be started with a temporary profile.
The preconfigured browser instance is a great feature, but I don't use it because the launched browser instance does not use my "Default" profile (with extensions, bookmarks, etc). It is possible to launch Chrome from the command line with arguments, including specifying the profile to use.
Would it be possible to include in the Fiddler Browser settings panel a field that allows users to specify arguments to be used when launching the preconfigured browser instance? Or if not then possibly just the profile name to be used?