One thing the RLA does is give time to the unions to get all the pilots on board for a strike. That can be useful, since pilots are loathe to risk their jobs (and no one wants to see their company go out of business), and it takes a while to get everyone on board in this country, unlike the EU where strikes and labor unions are just the same way they've done business for centuries. Their employees are much more used to that type of process.
Another thing the RLA does is prevent management from unilaterally imposing new work rules / pay rates on the very day that the contract is amendable, and forces them to go through the bargaining process or the court system in bankruptcy to obtain concessions.
Using AirTran as an example, back when the contract became amendable and we had a weak union on property (about 5 years ago), if there were no RLA on the day the contract became amendable, management could have walked in and said, "We're going to unilaterally cut wages by 20%, cut your B fund by 50%, and get rid of the Twomey/Casher award". The pilots would be up in arms, but afraid to walk off the line that very day. Then the company comes in at the last second and says "Unless you sign this new contract that freezes all wages for another 10 years, we're going to follow through with our cuts". It's possible it would have passed. Today is another story.
Now that we've had time to get our ducks in order, stronger union, more organized, and ready to fight that battle, management is in a much worse position to do any such thing once we're released into self-help.
So it's a two-way street. Yes, we'd get the ability to wildcat strike, sympathy strike, and not wait half a decade or longer for the process to work, but management at airlines that weren't prepared could seriously mess with the pilot group. It would require an entirely new method of preparation and operation by unions in this country.