Why Brewster?
A more traditional name is Ron. As in Re-Open Nominations.
Another one is NOTA. None Of The Above.
Also FEA. [expletive] 'Em All.
Yes, every election should have it. No, it's never going to happen, short of an armed revolution (and almost certainly not even then). The ones in safe constituencies would never permit it, because once RON is on the ballot their constituency will no longer be safe.
Even so, it won't work until we have something better than first past the post. Something using a Condorcet method is theoretically the best option but practicalities render it infeasible (you need to tally the votes by computer and few here would trust that). Some Australian elections use a method that can be done by hand and allows for preference voting. We definitely need that.