Really? Shut down public transportation, public health care, public telecommunications and public power? Do you have an equally brief transition plan?
Does the state's involvement in public corporation screw up incentives? Telecommunications is a good example of why not. Banks still don't convince me; they pay taxes with interest rates significantly less than 18-20%, which is the norm and they have resisted any and all attempts of the state for policy changes.
Personally, I am more concerned with other issues: the legislation that often proves to be shortsighted and inefficient, limited (and that's a euphemism) opportunities to young entrepreneurs, poor education, but the one thing that bugs me the most is that Greeks (yeah, I'm one of them) have no regard for public interest. The why is a longer story than what can fit in this post.
PS. You hinted to "shut down the money-loosing public businesses" as the "more appropriate solution"; if you're not advocating for it I may have to brush up on my English comprehension skills.
Beyond that, when talking about profitability, you should consider pension plans and future obligations. Some of these businesses might have a positive balance sheet for the year but what's going to happen if you consider their future, inflated, obligations. A good example are the pensions the Public Electric Company employees get. They are mostly funded by the government.
Let's see why it screws up incentives: -- What do you think any of the people working in the public sector tries to optimize? Is it the successe of the business they are working on? Do they try to advance their careers? Or do they try to work as little as possible? -- If an employee is not good, is a government controlled company ever going to fire them? -- The guy who controls the supplies in the hospitals, does he ever have to report to somebody about that? -- Do you know a single person in the public sector that he has ever been promoted or fired because of his skills or lack there of?
A point which I didn't make. Improvements can always take place. But no matter; not all businesses I was talking about are monopolies. In fact, the telecom sector is free since 2001, and it's doing great, considering HTO possessed 100% of the infrastructure up to that point.
Incentives are given by management. It is extremely easy for any business to motivate their employers, as it is easy to lay off slackers. It mostly does not happen; this is a result of corruption, incoherent legislation, and poor law enforcement as well as financial and management review (among others). I've already mentioned those factors, I view them as extremely dangerous for our economy and I highly doubt they'll be waived in any reasonable amount of time. I think we mostly agree on this part.