I have an idea. Imagine your username is “helloworld”. and for some reason instagram disables it (for example impersonation). After this you register “helloworld.com or .net” domain, apply to instagram, send them the proof of domain registration.
Even if it did work, no clue one way or the other, they could easily check registration date and see that was done the day of (or a few days before) and consider it a spam/hijacking tactic, although that’s not to say they’d ever investigate but maybe the admin backend has checks for pulling all sorts of data like that already.
Instagram won’t give an account back just because you created a domain name that has the same username even if they leave the proof up to you they still have some specific requirements that can prove you are the owner.