True, it's not a neutral trade-off because even if you smash the car in the first month, you're still out 1 month's insurance (assuming you didn't prepay the whole year). There's also the deductible to account for. We could figure this out mathematically:
Let c = cost of collision insurance per month,
v = market value of the car,
p = probability of at-fault accident causing damages in excess of v in a 1-month period,
d = deductible
If insured, your expected cost = c + p*d
If not insured, your expected cost = p*v
These are equal when c = p(v - d)
So let's give this some real numbers. Let's say your vehicle is worth $2000, and you have a $500 deductible. Let's say you hardly ever drive it, so the chance of you smashing it up in a one month period is 0.5%. Then c = 0.005(2000 - 500) = 7.5, which means that if the collision portion of the policy costs more than $7.50 per month, you should cancel it (mathematically speaking). This is of course a simplified method that doesn't take into consideration other probabilities like partially damaging the vehicle.
Insurance companies are in the business of figuring out your value of p, and using it in a similar formula to figure out how much they need to charge (c) and still earn a profit. You can be sure they pad their bets by a good margin, and of course they have operating costs to add in as well. So unless you are a much worse driver than they think you are, chances are the value of c will be higher than the expected value. The difference is really just the cost you pay for peace of mind (the psychological factor), and everyone puts different value on that. When you can easily afford the risk, you obviously don't care as much about the potential costs of a crash. But for a more expensive vehicle that you can't afford to replace, you might be willing to pay more for that peace of mind.