Not sure what's it's like in other countries but in the UK in terms of numbers of days lost the Public sector seems to have a far higher percentage than the private sector
On average over the last decade or so in terms of total days lost about 80% are down to the public sector whilst only 20% are down to the private sector. The number of industrial actions however is roughly the same .
Of course when the public sector strikes it has a direct impact on the private sector.
If Teachers go on strike, workers might not be able to work due to having to look after their children.
If public owned transport goes on strike workers migh not be able to get to work.
In the case of buisness in the private sector going on strike, people potentially have a choice to take their buisness elsewhere.
Public finances aren't a bottomless pit, they are funded via taxation. Most people want high wages and low taxes which are two opposites.
In the case of the private sector wages are funded via the services/goods that buisness sells, and people working in that sector high wages, and the consumers want low prices. Once again two opposites.
Now of course some are willing to pay preimum prices.
We can't always get what we want, sure I would love a 5% pay increase every year, but over the last few years given the economic climate what we got offered was a modest pay increase but in line with what I thought we would get.
But I'm not arguing that the right to strike should be removed.