The accident statistics (I can help find them if you want) are that accident risk goes down steadily until (IIRC) mid 60s, and only increases above the risk of 20-30 year olds at a very advanced age in your 80s.

There are two things going on:

1. Young people, especially young men are on average significantly more reckless than older people. This is a direct way in which age "grants you better driving capability" - you just become less of an idiot.
2. Young people on average have less driving experience than older people. That's not a direct result of age but it does correlate.

These are different processes but they can both be targeted for safety measures.