I've found the older cities I've lived in with much tighter roads have much better drivers as a result.
People know their distances and are hyper-aware of their surroundings because it is a necessity in order to avoid minor collisions.
In cities that are more 'designed' by traffic engineers there is ample room so people don't know the dimensions of their own vehicle and travel at greater speeds while letting themselves be distracted more frequently. The accidents that result are usually frame-bending as opposed to bumper replacements.
In a lot of older areas the roads were built just big enough for farm to market purposes[1] either officially (as in Texas) or unofficially. This resulted in narrow, twisty & curvy roads that encourage people to drive slower and safer.
The safer a road is perceived to be through visual cues (wider, straighter, less hilly, etc) the faster drivers will go. Hence why in Seattle and other cities dangerous (read wide, "safe" feeling) roads are being put on a diet, and going from 4 lanes to 2 lanes with a center turn lane and bike lanes (sadly usually unprotected). The same thing is being done in Denmark, where they actually add curves & planters to the roads to force cars to curve and feel unsafe, which ultimately results in safer streets for everyone involved.
Another strategy that I've heard has better results is eliminating sidewalks and getting rid of jaywalking laws, so that traffic of all types are forced to intermingle at much lower speeds.
As for mingling different sorts of traffic - I've heard of several spots here in the Netherlands where they've done just that, and it doesn't always result in lower accident rates. At some point you cross the line between "less of a comfort zone everybody is more aware" and "confusing mess that has so many things going on that nobody is aware of everything".
A narrow road can still be predictable - you'll have to be alert to prevent minor bumps, but there's no surprises that can result in rear-ends because you have to slam on the brakes.
I don't have any studies numbers to back it up atm.
My town has in the past year eliminated raised sidewalks/pavements. All that happens now in those areas is that cars drive all over the pedestrian bits and park on them. It's called a "shared space" but car drivers, being rather selfish, just drive and park wherever they wish with scant regard for pedestrians.
I've had several british friends tell me that if they pass cars in America like they do back home (say, within a foot with both cars traveling at 25-30mph), American drivers will go ballistic at them and can't believe at "how dangerous they are driving". The difference is that they have much better training and know that they can pass safely.
Come to Ireland and leave the motorway network for our country roads, we pass within inches of bushes on one side and cars on other at 80 to 100km/h while being blinded by idiots misusing fog lights and reflections of perpetualy wet roads. These "roads" resemble twisty tunnels thru trees :D
You should visit Boston or DC some time. It will be an eye-opener. Both are cities that were designed well before cars. Snowbanks make things even narrower. This should be urban planner paradise, given the much tighter roads.
As for the much better drivers though... well see for yourself.
In cities that are more 'designed' by traffic engineers there is ample room so people don't know the dimensions of their own vehicle and travel at greater speeds while letting themselves be distracted more frequently. The accidents that result are usually frame-bending as opposed to bumper replacements.