Reward race times rather than lap times with points.
You can place sixth, have come off the track a couple of times and still get more points because you had one good fast lap, than the person that did all the laps in the fastest time to win the race.
At the moment, winning the race is not as important as getting the fastest lap time.
As I was getting to the end of my Bronze license, I was racing more for points then position because I wanted to see it tick over to Silver. Rather than risk overtaking the slower driver in front of me, I'd hang back a bit so I'd have clear track between us, then with the nice clear track, I could concentrate on getting a single fast laptime in over the next couple of laps. It didn't matter if I let the guy in front of me finish ahead of me, I would almost always get more points because of my one fast lap.
I learned this from noticing I could be following someone that was faster than me, but I've slipped by them when they've come off or made a mistake. I end up finishing the race ahead of them, but they still would get more points because their fastest lap was better than mine.
Winning should always be rewarded with the highest points. I do only mean for the same license levels though. A race won by a Gold driver should get more points than any other Gold driver in the race. The Copper driver in second place may get more points than the Gold driver, but no other Copper or Bronze driver should get more points than them, just because they had one single fast lap.
And the race winner would still have to finish the race within 108% of the fastest race time to get any points.
What you could do is reward the single fastest laptime, just the one driver that did the fastest lap during the race, with a few bonus points for the race.
I believe this would in fact encourage even closer racing with less emphasis on a single hot lap, therefor less accidents, because everyone is trying for a dozen or so consistent laps.
Remember the Turtle and Hare parable. Your rewarding the Hare way to much.