Now that the idea is proven, there's nothing stopping more competitors from building local app driven services to compete with them.
If you can organize thousands of drivers, you shouldn't bother with a union. You should just have them collectively fund their own driver owned app and compete with uber instead of asking for crumbs.
Sure, it might not be hard to write a ride allocation app that works like Uber. But getting a large number of people to change their habits to use the new service instead of Uber will be hard. Just getting them to be consistently aware of this new option will be expensive.
As a first mover, Uber benefited from enormous amounts of earned press. An Uber clone today will not get so much free coverage, and will have to spend money on marketing. That is a significant barrier to entry.
That is actually a large part of the problem. Competition from Lyft will force Uber to lower fares. Competition from a driver-union-app would force them to be even lower.
At some point, lowering fares will directly hurt uber. Prior to that point, it's hurting the drivers because uber doesn't care at all about drivers costs, and drivers are either not good at taking that into account, or have been screwed by falling fares.