Anybody should be allowed to run. The point is he would not have had any support.
Without support from Greens/Left-wing voters, he would have no impact. Many people don't want to vote for a party than excludes their issues on trade/labor/environment/human rights/etc.
It does make a difference what positions the Democrats take, for people in this voting group. My sister is a good example. She is working her butt off for Green Party candidate Jill Stein in Ohio and keeps blabbering on about how we need a "Green New Deal" or some nonsense. I think if the Dems would have just paid a little more attention and taken on some of that Green/Left Agenda, we could have kept my sister's vote. She was an Obama supporter in '08.
Do you want only Democrats and Republicans to be allowed on the ballot?
I'm sorry some people think the lesson from 2000 is that Greens and left-wingers need to be insulted until they shut up.
The correct lesson is find a way to be successful with a challenge from the left. Either by run-off voting or adopting some key pieces of the Green/Left agenda. Because I guarantee you people are not going to shut up and watch the Democratic party get dragged further to right every election and just go along quietly.
PS. Nader uses left-wing talking points, not right-wing talking points, so what you mean?