I've encountered something similar at 2 dif properties - one, cut my foot on edge of bed because steel had broken off from edge of bed frame & one where I slipped & fell outside the front door (slippery shoes). Both were non-Marriott properties.
The first instance it was a casino property in Vegas that was packed to the gills with a convention, so I'm not sure they could have switched rooms but since I was the 2nd guest & not the primary one (my friend was) in the room I didn't think it appropriate to ask for room change. The 2nd it didn't really have to do anything w/ the property (which was a chain), but the shoes. Wearing the same pair I slipped/fell at LAX a few weeks later & broke my elbow. Got rid of the shoes after that (and they were flats, not heels - go figure).
In both instances they sent someone up to take a report, provide some basic first-aid stuff (ie, hydrogen peroxide, bandaids) & ask if I needed a doc. I think that's SOP for most hotels in those type of situations.
I probably wouldn't ask for compensation since the injury was minor, but I'd chat w/ the GM about the lackluster response of the first clerk.
PS - I walk across hotel rooms in my bare feet. Like you I assume it's safe to do so & don't expect glass shards. Of course I also don't wipe down everything w/ hand wipes either.
Cheers.