What if they allowed duplicate names? Navigating to twitter.com/username would then display everyone with that name (like how Wikipedia handles it). The chances that you are following more than one person with the same name is pretty slim. If that does happen, then you pick which one gets your @ replies.

One solution is to expose unique IDs and allow people to hang nicks on those. Using email addresses or phone numbers goes most of the way toward this (it's not all the way, since people could get an email address or phone number that someone else used to have, at some ISPs or phone companies). However, there's a larger, related problem, which is the problem of identity: there is no foolproof way of identifying individuals, and the more you investigate, the more clear it becomes that existing attempts fail miserably for edge cases, and criminal / fraudulent activity is probably the longest edge.

Isn't it the same issue as last year, and the last 10 years? Picking usernames etc isn't a new practice.