The benefit is that you can deal with a trusted driver rather than someone that takes 3 wrong turns on the way there then misses the exit for the airport.
You are missing the details here. OP is suggesting that they get an Uber/Lyft driver then instead of paying through the app, pay with cash. Same driver, just no insurance.
Paying the average amount means you're paying more than some fares.
By paying cash, you lose out on all insurance in cash of an accident.