Design isn't solely about 'being creative'. It's part of it, but a big part is about 'effective communication'.
What is the purpose of a resume? For the most part, it's to effectively communicate something.
A vast majority of the time, a resume should be a utilitarian tool. That doesn't mean it needs to be plain, nor that care doesn't have to be put into the design, but this is not the place to stretch your 'cleverness' or 'decorative' skills.
Your portfolio, on the other hand, that is where you absolutely want to show off your skills at creating visual flourishes and the like.
As for your specific question:
Is a résumé a vehicle for a designer to showcase skill in design? Or, is something with a simple message, good typography and clear hierarchical structure enough to stand out?
I don't see those as being mutually exclusive. Yes, a resume is a vehicle for a designer to showcase their design skills--specifically their skills of page layout, writing and typography.
I think what you perhaps meant to ask is: Are resumes are a place to experiment and being 'clever' to attract attention? I'd say they CAN be, but that's the exception, rather than the rule, and, IMHO, you have to a) be VERY clever to pull it off successfully b) targeting the right firm with the resume.