So my guess is that $cmd[0] is inspected for whitespace or quotes, and if it contains either, an intermediate shell is invoked.

That doesn't explain the difference at all. Both 'perl ' and $^X.' ' contain a space.

And there, quoting becomes necessary:

Not at all. You're mixing the single and multi-arg form for system. Quoting is not the bug. (It shouldn't work with quoting either.)