It could be a good addition to add a button in your profile like the change nickname button in servers which changes your nickname across all servers (which have nickname permissions enabled for you).
The reason for this is that for a lot of servers (particularly public ones) I want to use the same nickname instead of keeping it the same as my username or manually changing it. For example I recently changed my username to IbissalThoth to make it more unique but I prefer to use a nickname of Thoth in servers.
Another benefit would be that you could use this like how people do on twitter, altering their nickname with emojis or addition text for holidays and special events.
Overall I think it could be a useful addition (even if it is a bit niche) and it provides a shortcut to do something already possible and benefit people who frequently use the nicknames feature.