/data remove not working on non-primitive, non-list values

In my specific case I'm trying to remove a Leash attribute from a mob, but I have found this true for many other properties as well. The example below tries to remove a CustomName

Steps to reproduce:

/summon pig ^2 ^ ^ {Tags:[tpig],CustomName:"\"Oink\"",NoAI:True}
… Summoned new Oink
/data remove entity @e[tag=tpig,limit=1] CustomName
… Modified entity data of Oink

The second command says "Modified entity data of Oink". But the name is still there, displayed and in data.

/data get entity @e[tag=tpig,limit=1]
… CustomNameOink has the following entity data: '{"text":"Oink"}'

The following also doesn't work:

/data remove entity @e[tag=tpig,limit=1] CustomName[]
… Nothing changed. The specified properties already have these values
/data remove entity @e[tag=tpig,limit=1] CustomName{}
… Nothing changed. The specified properties already have these values
/data remove entity @e[tag=tpig,limit=1] CustomName.text
… Nothing changed. The specified properties already have these values

 Of course, I could remove (for example) NoAI. If only that's what I wanted to do...