I think there was restrictions in nip-01 at first. But it probably doesn't make sense anymore
If the username doesn't have restrictions then should we remove the display name?
Discussion
I don't remember any restriction in NIP-01, so I would safely remove it.
Display name has always been controversial, actually it does not make much sense, in fact I didn't include it in Nstart.
A lot of clients also started to deprecate/remove it.
what is display name?
Check the protocol.
NIP-01 (the core and mandatory part of Nostr) prescribes usernames (the "name" tag), but allows for additional metadata fields, which are described in NIP-24. Among them, the "display name" (the "display_name" tag). The "name" tag should be present even when the "display_name" is not, but not the other way around (although I think if only the display name is set for a user clients should display it).
Personally, I don't think they were a mistake. I think there are arguments against it, but also that they do have some use. Essentially they serve the same purpose as usernames, but may have a different style.
The presence of both the "username" (which, unlike on other platforms, is not identifying and not unique) and the display name doesn't make a lot of sense, indeed, and I don't know why it was ever a thing.
However, you are free to set one and not the other (I think a client should display whichever one you di did set) or set both to the same value (which I see many people do).
I think it makes some sense to have both fields, although it may be confusing, because people can set them to different values: a short, one-word original nickname as a "username" and a longer, possibly less original, name as a "display name", which may be your real name (if you are not anonymous). I believe there's something similar on IRC.
Clients can display one or the other as the primary name for a user, depending on the style they want to have: you want a HackerNews feel? Show usernames. You want a Facebook feel? Show display names.
For example, my username is "Apsie96", but by display name is "Valentino Giudice", my real name. There is no rule to follow and I could even have swapped them, but I think it's better this way.
While I might have opposed the double field, for essentially the same meaning, I'm actually not against the presence of display names for this reason.