I had quite some beef with the tethered caps in the beginning when they didn’t latch properly, but have since gotten used to them. That said:

• Cap on top -> Funny hat for nose!
• Cap on bottom -> Beard gets to take a moist nap.
• Cap on sides -> Mustache also gets to take a sip!

Obviously not much of a problem. I’d need to clean my facial hair either way if eating ice cream or other messy foods, but cap rotation might not be effective if your “face” sticks out 1-2cm from your mouth.

One could also attempt to rotate the cap in a way to achieve quantum tunneling, but I don’t feel that I’ve achieved that level of “tethered cap proficiency” yet.