> the left has much more societal power than the right
If we're speaking about the US (and we are), this is so far from a realistic view that no one will take you seriously for espousing it. Even if you believe this, I would recommend that you hold back on stating it in discussions like this.
If the US left existed meaningfully at all (it doesn't, we are an incredibly niche group), we would have universal healthcare, a minimum wage indexed to inflation, bankers would have gone to jail over 2008, and thousands of other things that have demonstrably not materialized. Hell, the Democratic (supposedly the "left" party in our rigged system) president recently forced a contract on union railroad workers against their will. This is just about as right-wing/pro-capital as a policy can be without calling for a formal return to serfdom.