In theory, when there is only one customer for the service, prices will be artificially low, not artificially high.

As a clarification: You mean in the absence of a negotiated contract that allows the price gouging the government often gets handed in the deals it negotiates, yes?

But when you privatize a public utility you have many customers and a single provider - the exact opposite. Hence higher prices and/or worse service.

The top level comment was pointing out that privatization isn't necessarily the issue, it's that the government picks one company, and hands them a monopoly. That is what creates the situation you're describing. I have no idea why it's done this way (without devolving into pure cynicism). I guess maybe it's easier to administrate? And it allows the government to technically still own the utility, which they've just farmed out? Once you let a bunch of businesses take over, you're never really getting it back. The real answer is probably just: Laws.

Assuming the supply is competitive sure ... Otherwise you're in the worse of both worlds.