...as long as publicly-run entities ... are part of the competition, they distort the market,

So what? "Helping companies to make a profit" should not be the ultimate goal of a democracy unless the people decide so. Ultimately, the goal of the government, which are elected representatives of the people, is to do whats best for the people, not whats best for the corporations. If that means running a costly service so everyone gets their mail and everyone can afford to send mail to everybody else, then so be it.

It is certainly possible for a corporation to take over running such a service. But than it should be required by law to hold to the same standards as the former government service. That includes government prescribed maximum pricing, a service that is accessible and affordable by everyone. Prompt delivery. Postal secret. And so on.

What many in investors don't undertand (or don't like to understand): Essential services like post or electricity and such are... well essential. You can't just cut of areas that make a loss or demand huge sums of money for service in this area.

It is also my very personal opinion that you can either run a government operation or a private corporation. When the next "too big to fail" company comes along to get the government to pay for their losses: "Fail, loosers!". If this would cut essential services, just let the government take over the operation and give the shareholders: Nothing. They failed to run a private corporation, so the only thing the people (or at least the managers of that corporation) deserve is jail time.

Same goes for banks: Don't save the bank, save the customers (at least the ones that didn't gamble their money on high risk investments). Save the grandma that may loose all her money she saved for the last 60 years. Don't save the bank. It is an institution that failed, if you save it you'll have to do it in a few years again. And again. And again. Because they can risks everything they got and they know you'll save them if/when the fit hits the shan.

Note to politicians: If you send the managers to prison and save Jane Grandma, you saved the economy from collapse and from a few gangsters and you'll probably get re-elected. If you save the bank and send Jane Grandma to prison for not paying her bills, you'll probably go to hell or whatever unpleasant afterlife-equivalent you believe in (if you don't believe in afterlife, we can always send you as foreign minister to Siberia. Sorry, we don't have a budget for heating, lost it in some bank saving deal that went belly-up).