It may seem rather odd to say this, but it is actually true that Keynesian Economists are not automatically advocates of the regulatory state. By definition, Keynesian economics is concerned with fiscal policy, using federal budgetary policy to moderate the economy. There is nothing about that which would indicate that a Keynesian must embrace regulation - it is theoretically possible to encounter a Keynesian who is only concerned about fiscal policy.
The reason it appears that Keynesians must be in favor of regulation and the attendant bureaucracy is because all Keynesians are. There is no economic activity they are content to leave alone.
The right-Keynesians and the left-Keynesians differ on who should be the beneficiary of the demand pushing government spending. Right-Keynesians would prefer to benefit the upper classes, leading to supply side economics as the outgrowth. Left-Keynesians prefer to benefit the lower classes, leading to demand side economics as the outgrowth.
The unnecessary (from a textbook point of view) embrace of the regulatory state has a similar division. Right-Keynesians prefer regulations that benefit the upper classes, leading to Mercantilism or Corporatism as the outgrowth. Left-Keynesians prefer to benefit the lower classes, leading to Progressivism as the outgrowth.
When cornered in a debate, it does happen occasionally that Keynesians will admit that regulation is not part of Keynes’ General Theory. Perhaps it would be more interesting to corner the Keynesian on that and try to force an admission about how far from Keynes’ writing they have gone in their embrace of regulation.