Easier firing would increase the market rates for every role. At least unless combined with generous unemployment benefits, as in Denmark. It could make the government more efficient in the long term, at the expense of higher spending (and therefore higher taxes) in the short term. Which many voters would not like.

The issue with unions negotiating with politicians is mostly a consequence of an excessive number of political appointees. Many things would be cleaner with more career civil servants in top positions. Top officials would have fixed-term appointments, and they could not join unions or be fired without a criminal conviction. They would run their departments, while political appointees would only set the goals and directions with little direct control. And then the rest would be more like ordinary employees who just happen to be working for the government.

Government employees are a mostly irrelevant category anyway. Depending on the time and place, the exact same job can be performed by an actual government employee, outsourced to a private contractor, or done by an employee of a company fully owned by the government. What the employee can or cannot do should depend more on the actual role than on the administrative structures above them.