Except the only reason taxis can "show that they matter" by shutting down is because they've been given a monopoly from government (via medallion system).
The result of this monopoly, at least in San Francisco, is a shortage of cabs, poor customer service from cabs and high prices.
All this strike proves is that no matter how good they have it, they'll always ask for more.
The fact that cab drivers also managed to form a union means nothing other than they're smart because they can leverage that to get a good deal for themselves (at the expense of every other person living in San Francisco). Forming a union doesn't suddenly entitle them to anything.
Uber is a long due competition to cabs. It improves the lives of people living in San Francisco. If cabs can't compete, then they deserve to lose and Uber has every right to compete with them.
That is the point of capitalism: ability to compete. Taxis don't deserve special treatment. Neither does Uber, for that matter.
There's a difference between being anti-union, and anti-medallion. I like taxi drivers. It's not their fault they have to pay hundreds of thousands for a medallion, and work with a lot of overly strict rules.
AFAIK, these strict rules don't stop taxis from screwing over tourists, and occasionally assaulting customers. I'm pretty sure an Uber system would, as the bad eggs would be tracked down a lot easier.
If unions want to protest unsafe cars, or 14 hour shifts, or they want the right to refuse service to unruly customers, that's fine. It's not a simple matter of supply and demand. But unions shouldn't be locking other workers out.
I'm pretty sure they are actively campaigning against increasing the number of medallions, so yes... they are to blame for making it a scarce resource and therefore worth hundreds of thousands of dollars.
You make it sound like taxi drivers are doing charity work. They hold hourly jobs just like 80% of San Francisco. Of course taxis matter, that's why they exist.