In the US, your name would be on a master list...but then again, we invented it, YOU perfected it...
Well, the US has a truly common market, the EU doesn't. We can't even represent all pilots with the same union, even if we wished to do that. We have to have a union in each separate state. And each separate state has separate and different employment laws, some are very open to industrial action, some are not, some pretty much have outlawed it alltogether.
Now picture that each US state has to have its own pilots union, even if all pilots are employed in one company. That the employment laws are different in each state and most do not allow to refuse work even if the pilots of the same company working under a different contract in a different state are on strike.
Of course, pilots could call in sick. The first time that happens it will go through, the second time it happens each separate union will be sued for an illegal strike, in most states found guilty and liable for any damages the airline has suffered.
As a union rep i have to deal with the conditions we live in, not some phantasy ones we wish we had. Yes, last time i was organizing a strike action i couldn't do anything against the fact that all of a sudden a lot of austrian registered aircraft sat on the tarmac in germany, their crews in the hotel just waiting to take over. And i don't blame those crews, they had the choice between working, or never working for that airline group again.