This question now has a new answer!
On November 4th 2019, the Class Feature Variants Unearthed Arcana was released.
This UA includes a variant rule for every spellcasting class that has cantrips, that allows them to swap them out, either on long rest or on level up.
Bards, Sorcerers, and Warlocks can now swap them out on long rest:
Whenever you finish a long rest, you can replace
one spell you learned from this [Spellcasting/Pact Magic]
feature with another spell from the [bard/sorcerer] spell
list. The new spell must be the same level as the
spell you replace.
Since cantrips are spells, this means you can swap cantrips out for other cantrips. This is specifically called out as possible in the same UA:
Rule Tip: Cantrips Are Spells
Cantrips are 0-level spells, which don’t use spell slots.
When a feature applies to spells, that feature applies to
cantrips, unless the feature specifies that the spells
must be of 1st level or higher or must expend a spell
Clerics, Druids, and Wizards can swap them out on level up:
Whenever you gain a level in this class, you can
replace one cantrip you learned from this
Spellcasting feature with another cantrip from
the [cleric/druid/wizard] spell list.
So the spellcaster in question might only have to wait one long rest to get rid of their redundant cantrip. Or perhaps they will have to wait til they level up. But in either case, they won't be stuck with the redundant cantrip forever.
To be clear, this does not allow the Arcane Trickster to swap out their Arcane Trickster mage hand, but if they have mage hand from another class, that is what they can swap out instead. This is a better option anyway, since the Arcane Trickster's mage hand is superior to a normal mage hand.
As always, ask your DM to confirm that they are okay with you using these variant rules.