You don't think a cabbie using Uber knows that there is an electronic record of them picking up a passenger? If anything, Uber is safer than yellow cabs.
But lets suppose this really were an issue. There is a simple solution: charge each taxi a flat $10k/year license fee (with no cap on the number of licenses issued). Use the proceeds to hire full time undercover taxi inspectors.
That gets you about 1 inspector for every 10 cabs. Assuming each inspector rides 10x/day (i.e. 5 hours/day riding, 30 min/ride), each taxi will be inspected every single day on average.
But lets suppose this really were an issue. There is a simple solution: charge each taxi a flat $10k/year license fee (with no cap on the number of licenses issued). Use the proceeds to hire full time undercover taxi inspectors.
That gets you about 1 inspector for every 10 cabs. Assuming each inspector rides 10x/day (i.e. 5 hours/day riding, 30 min/ride), each taxi will be inspected every single day on average.