The chances of crashes might increase, but the speeds would be lower, so the severity of crashes would be diminished. Instead there would be lots of spins under braking and people running off the road (even more than usual). Formula One races in the rain, and part of the excitement and strategy is when to switch from Dry tires to intermediate wet to extreme wet tires. Do it at the wrong time and you are stuck with a tire with no traction, or one that is slower than is optimal for conditions. It absolutely would separate the great drivers from the merely good, but it would also introduce another variable that can really shake a race up. (IIRC in the 2007 European Grand Prix an 18 year old, in his first race, in the slowest team on the grid, led for a while simply because his team made the best decisions on tire selection).
On top of adding variables to the racing, driving at the scheduled time would have a positive impact on NASCAR's licensing agreements, as they would be able to guarrantee a TV audience for their race. If you tuned in on Sunday to watch the race from the Glen, you probably ended up watching Golf, or sometihng else, instead of whatever ESPN played in the place of the race (I think it was just a couple analysts interviewing a series of drivers....).