In general, strike is a tool labor has against capital. Just because capital happens to be provided by taxpayers, how does that warrant a special case handling?
This is pretty much why there are very few public school computer science teachers who do a decent job, since the ones who can legitimately write code can get a much better job at a private company.
When you factor that they only work 2/3 of the year, the value of their pension and healthcare teachers actually make a considerable amount of money.
That being said I’m not sure what the right amount is - I put a great deal of value on education - then again the best private institutions probably pay less than public ones at the k-12 level
When government employee unions negotiate with their employers, they negotiate with a political actors who, if they act right, get support from the union for their next re-election.
The incentives encourage political actors to bend to the unions will to receive donations or endorsements in their next election.
Typically this is called a conflict-of-interest.