No, it's more like one year or less[1]
> I would bet a lot of people hit "something" that often
That's quite a claim... just from personal experience, I'd wager this is a very wrong assumption. Majority of people go most of their lives, if not their entire lives without hitting "something". More serious incidents are even more rare.
My collision insurance is $270 a year, which I think is fairly reasonable for NY. I was involved in an accident a couple years ago where the corner of my car was smashed in a bit, pretty much the definition of a "fender bender". It cost about $3500 to fix, and if I had been at fault, I would have had a $1000 deductible. Repairs could have been $2500 if I was more lucky in exactly what was bent. So, that suggests my insurance company breaks even if I go about 5-10 years between at-fault accidents, or 75,000-150,000 miles. In the aggregate, I assume they do estimate risk pretty accurately, so I expect that 5-10 years is normal. Whenever people mention what they are paying for insurance, it usually seems to be higher than mine.
That's almost surely because of your $1000 deductible. That's very high... mine is $100 for just one reference point.
> So, that suggests my insurance company breaks even if I go about 5-10 years between at-fault accidents
That would be a "break even" point, but insurance companies attempt to turn a profit, so this suggests they expect majority of their customers to not have an event every 5-10 years, but on average a longer interval. They also account for non-traffic accidents, such as vandalism, broken window, theft, etc... none of which involve the driver being "at fault" or hitting something, which was the original assertion by the GP.
The non-collisions aren't relevant because I quoted the price of my collision premium only and not comprehensive or liability. That was on purpose, to be consistent with the topic of "hitting things" and with the sort of fender bender I was talking about.
Profit is not very large relative to premiums, so "breaking even" is a reasonable simplification. For example Progressive (not my insurer, just the 10-K I was able to find the quickest) made about 6%.
Not at fault accidents are some other companies "at fault" accidents, so counting them is double counting and would inflate my estimate.
All I'm saying is that, without false precision, evidence suggests people hit things every 5-10 years on average. Having an accident every year or never in a lifetime is not normal.