I don't believe all political parties have a right to exist, because some parties are anti-democratic, yet abuse democratic systems to gain power. The current president of the US and the organization that planned the current administration's steps are anti-democratic and want to, for example run for a third term.
At personal level that sounds like a better idea, but at group level it doesn't seem to be, that's what I think is OP's argument.
If a society puts more value on personal freedoms than it does on group well-being that becomes an anarchy. They didn't work out well historically speaking, proof is no such society made it to today.