The deck is stacked against a third political party. We should stop fantasizing and accept that.
There is one avenue to reforms that can curtail the dominance of the major party duopoly that Mr. Cohen doesn't mention -- the initiative process, which is available to bypass legislatures in about half the states. It's notable that open primaries (CA, WA) and ranked choice voting (AK) have been enacted via citizen ballot measures. This is a path to reform that can help clear the way for third parties.
Thank you for your essay.
Now I am sad.
Impossibility? Nonsense. This ossified system is cracking and ready to crumble. One dynamic leader could take it down. This leader will appeal to common sense, which still exists and for which there is strong hunger. No tepid fence-sitter, he'll rain fire on the excesses of both parties and their unhinged ideologies, rightly laying the blame for most of our civic mess on them. He'll sell competence, growth, basic decency, effective environmental practices (such as carbon pricing and nuclear). He'll promote state's rights on the most controversial social issues, thus avoiding those traps and leaving an outlet for fanatics of both parties. Business will back him, once they see his movement is for real. So will 30-40% of the body politic, maybe more. Deals will be done with the most rational of the two old parties on any given issue. Extremists will thus be marginalized. Institutional bars of entry? They'll be swept away like decrepit seawalls in this fluid, digital age. One talented, centrist leader can start that tsunami.