Never give your actual address. Pick a house number a few down. Especially if getting picked up to go to the airport. Some rogue/criminal taxi/uber/lyft drivers will ask questions about your trip to determine if your home will be vacant and for how long to pass the info onto someone else who will come by to burglarize your house.
A cab driver using a much cheaper service vs. the rent-seeking credit card processing they are mandated by law to use? That's a morally correct action. The immoral action (imo) is to continue to feed into the fraud that you yourself identified earlier in the thread.
I have very little problem with a cab driver doing this, just as I have very little problem with you reporting it for the reasons you mention.
And having a rather interesting early start to my career - I assure you "native" citizens get away with this kind of crap all the time.
What percentage of the population do you think scrutinizes every credit card statement line-by-line? Many people would not notice an unauthorized charge on their card. It's merely a matter of scale: some people will notice a single unauthorized charge for $5, while others won't even notice $500. Credit card fraud is rampant, and any company that willingly allows its employees to get away with it should be shut down. My experience shows that my city's taxi companies consider credit card fraud as something that doesn't even register on their radar. Drivers that operate in this manner should be criminally charged. It's not just fraud to the taxi company - it is a criminal act of theft for the customers.
At least in SF, I'm pretty sure the standard deal is that the drivers pay for the cab regardless of what they get in fares. Cabs were a cash business for a hundred years, after all.
I think the deal with credit card machines in the cabs is that the cab companies see it as a revenue source. I know cab drivers grumble about the cost of using them. It makes sense to me that Stripe is cheaper for the cab drivers.