I understand bragging rights, but it's pretty hard to brag with something noncorporeal. That profile pic? Anyone can use that, whether or not they own the NFT or not. Makes for some pretty poor bragging material if you ask me.
Except copyright and trademark laws exist. The Washington Redskins lost their trademark. You can create as many NFTs of their logo as you want. But you cannot stop me from putting that logo on my website.
Currently yes, but that's a fixable problem.
For instance Twitter could start preventing users from having profile pics that look similar to NFTs that were minted earlier.