The argument isn't that the left broadly construed opposes housing legalization! Just that there's a prominent faction of them that do. Right-NIMBYs are a much bigger problem across the US.
Thompson recently recorded a podcast episode with Zephyr Teachout, taking the "we shouldn't do anything before we address antitrust" side of the argument; you can listen to it if you think "the antitrust left" isn't a real thing. Understand: the issue isn't antitrust; it's a totalizing worldview based purely on antitrust. Antitrust is probably super important! But where I live, zoning reform is much more important.
Keep in mind: Klein and Thompson's political project is a plan to organize the Democrats. They're not talking to the Republicans. Not in the sense they're talking to Democrats, at least. I don't think they could make that much clearer than they have.