Question: I am planning to do a one price lease to save money, but I am concerned that if the car gets totaled early due to an accident or gets stolen, I would lose a lot of money. Am I right? Is this generally a bad idea due to the risks I have outlined?

Please note that even though I can afford to pay the entire lease upfront, I am unwilling to buy for several personal reasons.

Answer: 
If you are looking to save money on car ownership, leasing is the most ineffective way to go about it. I would imagine one price leasing is even more inefficient than the typical monthly scheme. The specific question you are asking would be highly dependent on the leasing contract, so it is impossible to answer. In order to make it equitable for the buyer, there should be some provision for an early lease termination regardless of the reason.

Presumably you have the cash to pay an upfront lease, so you have the cast to buy a car outright. Buying a gently used 3 year old (at least) car with cash is the best way to save money on car ownership.

The biggest cost in car ownership is depreciation. With leasing, you are not only paying the depreciation but also financing it. With up front leasing, you are probably ending up with an even worse deal. By buying a three year old car, much of the depreciation has been already paid, and if you own that car a long time, the depreciation per month becomes rather negligible. 

If you are really wanting to save money, buy an even older car. Almost all of the depreciation would be paid, the cost will be low, sales taxes and licensing fees would be low. I like to aim for cars in the 4k range. Even with repairs these cars typically have a far lower cost of ownership then buying nearly new.

It all depends on how much you hate money. If you really hate money, then lease.
Coverage from 'if the car gets totaled early due to an accident or gets stolen' should be handled by your insurance. Seems to me that you need to make sure that your insurance policy properly accounts for the all-upfront-lease and some equivalent of gap coverage (which comes from when you enter a payment plan to purchase a car, but due to rapid depreciation of very young cars and the higher proportion of interest on early loan payments, the loan principle can be higher than the net value of the car, the gap coverage protects from that) for up-front-leases. These sound like questions for your insurance agent, all in all.