Busting the myth of the "scofflaw cyclist" Danish Road Directorate studies reveal that while 66% of motorists routinely break road traffic laws only 5% of cyclists do so. Law breaking by cyclists is higher where there is no cycle-specific infrastructure.
Some interesting stuff here, including links to more studies showing similar results in different countries.
The summary is that the reason motorists break more laws is that speeding is so common.
I don't think this is because motorists are all evil and cyclists are all saints. Probably, the reason motorists break speed limits is that it can be relatively difficult to keep cars below the speed limit. It's all too easy to absentmindedly speed up. It's also, perhaps becuase of this, widely seen as socially acceptable to break the speed limit (speaking anecdotally).
One interesting thing here, which may not surprise regular readers of Fuck Cars, is that better cycling infrastructure leads to less lawbreaking by cyclists. As is often the case, it's the design of roads and cities that changes behaviour, not abstract appeals to road users to be sensible!
Yes, drivers absolutely should be actively driving, but they don't. I've watched how a lot of people drive over the years, and the vast majority of drivers aren't actively checking their mirrors, and gauges every few seconds. Road designers have decades of data on how to subconsciously make us slow down. It won't stop all speeding, but it will drastically reduce it in the US.