I think they want the power megacorps have but under the umbrella of the government.
Luke Smith explains the book Capitalism, Socialism, and Democracy which talks about this. The only difference between what they envision and now is which institution is on the board of directors' paychecks. This is why progressives and many breadtubers want the EU and US Federal government to have ultimate authority over all matters within their states. I'm sure you know that, though.
I don't think I've ever met an anarchist that wasn't a complete statist a la Mao or a malingerer weed smoker wanting a government stipend for drugs.
And many of the small businesses destroyed during the riots didn't rebuild and didn't receive insurance payouts like leftists claimed would happen. It was a cope by leftists to justify destroying other people's labor.