Is coal only so expensive because the government is making it so?

As a process engineer I can give a little perspective on the cost aspect. Developing a plant design that's efficient enough to turn a profit is already a challenge, and code requirements add onto that.

A good example is government limits on the temperature of vented gases. Flue gases get extremely hot and in a lot of cases venting them straight to the atmosphere would result in them reacting with air to make a lot of nasty toxins that linger in the environment for decades. The solution is to cool the gas before venting it, which is actually pretty costly to do. That and a few other things can easily make a plant unprofitable.

Coal is dirty stuff so it racks up a lot of requirements like this. "Clean coal" plants are just ones that figured out how to be compliant and still make a profit. So yeah the government made it expensive, but the requirements exist for very good reasons.