Huh. I find it annoying because I'm usually watching for the car once I get the text and so extra time after being told "I'm here!" feels longer (it's like having a recorded announcement break into the hold music on a phone call), but also I think because I had assumed that they were getting somehow tracked on how long it took them to get to the pickup and they were gaming it by making the signal less useful to me. I know it's not increasing my trip length, thanks!
The actual paid portion of the ride doesn't start until you enter the vehicle and the driver taps the Start Trip button.
You can also verify the entire trip later on your receipt. It shows the entire trip on a map, plus the start and end times, so you can verify that it matches your expectations.