Privatization can still make a profit and be cheaper.

The only way I have ever seen that done is by reducing product quality or level of service. It is economically impossible to offer the same level of service and product quality at a lower price, all things being equal. Sacrifices are always made somewhere along the way by the private sector to achieve what you're describing. More often than not, the cost is much higher due to the reason I previously described. As just one example, consider how much Haliburton charged after taking over key services that the U.S. government once handled during times of war. Are there exceptions to what I've pointed out? Yes.

I agree with every example you just pointed as being instances where the private sector is currently better at handling certain projects/tasks than state and local government. I don't know whether you noticed or not, but the reason for the greater efficiency in all of your examples revolves around two concepts that the public sector could bridge if it was so inclined...Economic Value Added (EVA) and logistics. If state and federal governments pooled their resources, planned their projects carefully and coordinated manpower and equipment logistics, they could achieve greater economies of scale than the private sector, attain the same efficiencies (or greater) and save a lot more money for taxpayers than they presently do. It's not that its impossible for the public sector to be better at those tasks, it's that the effort hasn't been expended to create it for a variety of reasons.

On a side note, there would have to be a few labor practice changes in the public sector to incentivize that workforce to perform better than it does presently. In the absence of incentive plans, employees always behave less efficiently and effectively than they are capable. This is an area where I have seen both the private and public sectors screw up...the absence of an effective incentive plan or poor management of an existing plan. It always dings performance.

It's much more expensive to build a new company than to just expand on an existing company. Even after profit is calculated.

I completely agree since one has much higher startup costs. At the end of the day, it's best to choose the most effective and efficient choice, economically speaking, whether one is talking about the public or private sector since we're all footing that bill.