The assumption that people oppose these socialist ideas because of branding and not because of the empirical evidence that they don't work is an humble take.
Empirical studies show the opposite unless you want to swallow fabrications and lies by the likes of the AEI or the heritage foundation. They only exist to manufacture bullshit.
They need their own journals and publications because the sponsored content they call research can't stand up to academic scrutiny. They'll flip flop on their "conclusions" all the time because different people pay their bills.
They start from an ideological position, which is based on who is paying them, and then work backwards using reactionary arguments, misrepresenting statistics and sometimes just straight up fraud
I can't emphasize this enough. Think tanks are private propaganda factories and that's literally it. They're peddlers of agenda and ideology who are not concerned with reality.
Calling it "the other side" is a false dichotomy. There's certainly advocacy groups like Sea Shepherd but they don't wear cloaks of subterfuge to try to distance themselves from their structure and purpose like say, the heartland institute which among other things, was, at the time secretly, funded by Philip Morris to deny that smoking had health impacts.
That's a different class of spin. But sure, the Brookings institution is mostly neoliberal radical centrist, fine.
Well then I guess the other side operates on social media/etc and pushes ideas like we should give up our public spaces to homeless encampments and police aren't necessary. Or things like rent control, all of which do not work, ever. I don't think the reason "leftist" policies fail to gain traction is because of think tanks; the ideas are just bad and reek of armchair socialism/virtue signaling.