Unions are powerless in the US. Only 12% of the workforce is unionized. So, this argument that they have some kind of unfair advantage simply isn't true. These strike laws don't apply to 88% of the workforce.
Those who aren't represented by unions, doing the same jobs, tend to have lower pay, less job security, work harder, and have fewer benefits if they have them at all.
Furthermore, entire segments of the service economy, like janitors, fast food workers, and others, don't have unions. Most unions are out to protect middle class jobs like teaching or nursing (which only recently started organizing home health care and orderlies).
It's true that unions can abuse their power, but in my experience, the unions are always getting this shit end of the stick. The Reagan administration, and even the Clinton administration, were pro business and anti-union. The unions have little political clout. Strikes still end with pay cuts in exchange for retained benefits and job security. Sometimes, the unions sell out the future members by locking in high wages for todays workers in exchange for low wages for new ones.
If anything, the unions need more power. They're the only group that has any kind of power against the severe attitude of the corporations toward their least skilled workers.
If you're a capitalist, with a couple million in the bank or tied up in property, it makes sense to be against unions. If you're selling your labor for money, you should support unions, because you're a worker.