There are lots of UI problems involved with car insurance - some are (in my opinion) actually fairly interesting. In established comparison markets outside the US the big players invest a lot of money in getting the user experience right so that users complete the process (there is a large drop-off).
By far the easiest way to solve this is to do a registration plate lookup: however, I don't know if this is even possible in the US, and it would be on a state-by-state level so a bit of a nightmare. In countries like the UK, where there is a single source of plates that companies can buy access to, it's a lot easier.
Leaky could probably learn a far bit from how insurance quotation engines in the EU and other less complex markets handle this. Here in the UK there are many well established players doing what Leaky do, probably with more success (which is totally down to the fact the UK insurance market is much more centralised).
Registration plate lookup would be a chicken/egg problem here in the States. You need proof of insurance in order to get your registration, so on a vehicle that has no plates, there's no number to give, so wouldn't be able to get insurance. VIN is really the way to handle it, and once you get through the "quote" stage to actually buying it, all the insurance companies can take any VIN (and your info, of course) and spit out how much it actually costs. On a state by state level, I don't imagine it would be difficult to build a system to accurately compare rates. The fact that each state has its own system of minimum requirements, as well as what can be covered, and insurance companies are isolated to a single state (the larger insurance providers are actually corporations with wholly owned subsidiaries in each state) increase this complexity when dealt with on a national level. It's extremely similar to the issues with comparing health insurance plans.