I happen to be somewhat familiar, since I've been living there for 26 years. The majority of state enterprises (or those the state has a share in) right now are profitable, with the notable exceptions of a) railroads and b) the off-the-books units created by ministries to handle short-term tasks. Could they benefit from a restructuring and would lay offs be helpful? Probably so.

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.