The problem is not with democracy per se, the problem is that our "liberal democracies" never democratized the economy. Unless you democratize the economy political power will be invariably coopted by, basically, the 1% (what you describe as crony capitalism, but which is just capitalism).

You can control corporate power with regulations as you suggest, but we have seen what happened after FDR: corporate power was shackled to a degree but it started a slow but steady attack and is now wreaking havoc again. Capitalism cannot be shackled, it will undo any regulation given enough time. The real way to combat corporate power is to prevent them from being so powerful in the first place, ie. democratize the workplace, democratize the economy.

EDIT: The Chomsky of course says it better