I understand your feelings about the average taxi driver driving unsafely but there is a solution.
https://www.namstaxipattaya.com/
Nam's taxi service consists of 20 - 25 ladies and you cannot go wrong using their service. I personally would suggest requesting Yuri as your driver. She has a very new Toyota Camry she uses and it is pure luxury. Yuri, who has driven me on a number of occasions, acts more like a personal assistant than a taxi driver.
Driver (Yuri) always shows up early and I always got to my destination on time. She speaks excellent English.
Yuri is the lady in the front row, third from the left. She's a genuine sweetheart. Make your reservation by email and it will be confirmed quickly by email.