I believe others have reported the same experience. To finish in the top 3, you likely need to be multiple seconds faster than the fastest car on the track. That is obviously not a very realistic way to race, but neither is a 3 laps race. That's just how the career mode is set up. As a result, it appears a lot of drivers may be turning off the damage and smashing their way to the front, thus creating drivatars that are unbearable.
I abandoned the career mode a long time ago, and use the Free Play mode instead. You can set more laps, but the grid is set by PI as a default so you're almost always starting in front.
Alternatively, you could hook up with a club or team that hosts races, so that you'll get more clean drivers in longer races.