And private sector bureaucrats have an incentive to deny coverage, purge rolls, etc. - it means greater profits. In the last twenty years, health insurance companies have gone from spending 95 cents of every premium dollar on health care to roughly 80 cents today. Where did that extra money go? Greater overhead and profits. Under a universal system, public bureaucrats wouldn't have the same incentives to deny care.
Just a friendly reminder that before you start spouting cliches about "bureaucrats ruining things" you should ask whether they already have - just not from the government.