I'll add a voice for base58 representation of UUIDs on the wire, it's my preferred solution as well.
Not only for debugging: by being compact, unambiguous, and URL-safe, the helpdesk is also spared a cringeworthy source of PEBCAK incidents since misquoting the identifiers is simply harder.
Caveat programmer, though, there is a hazard, occurring when someone is glib about the usage and relies on randomly generated fixed-length base58 values directly. It happens readily because some popular frameworks include such generation as a utility function. However, 58^22 > 2^128 > 58^21, so a 22-character base58 representation is expected for UUIDs but carelessly random 22-character base58 values may exceed the capacity of UUID's familiar hexadecimal serialization, effectively an integer overflow. We never generate base58 identifiers as a PK, for example, for this reason (they would of course not be UUIDs either). Alas, there is no conventional base encoding more compact than hexadecimal that is robust to the general problem. And I mention it because this issue was observed in the wild.