The capture the state part seems to be spot on. You just need to take a look at how much lobbying goes on and our inability to deal with issues like climate change thanks to the big oil companies.
Edit: There are probably even better examples of lobbying than climate change as that has a ton of confounding factors that make it hard to deal with besides just oil companies. But I see no reason to assume distributism would make the issue better. Taxi drivers protesting against Uber comes to mind.