I have a 1978 Datsun/Nissan 280Z. Only one insurance company allowed an online/unattended quote for insuring that age car. Only one other company was able to give a quote after talking with them on the phone, all of the others didn't have the ability to do a quote, even for liability only insurance. I went in person to several places and the result was the same. The company that allowed me to get a quote online now has all my other insurance related business (renters/property/full coverage on my new car/etc.). It just so happens that they've been an amazing company to work with, particularly when we've had car related issues (getting rear-ended while stopped at a stoplight, hitting an animal in the middle of the night when there was no room to swerve/stop and rendering the vehicle undrivable, etc.).
Trying to go through the process to see what things are like, the list of makes of cars is an abomination. It tries to filter based on years the make was available, but isn't inclusive (Nissan starts at ~85, but Datsun doesn't exist for older dates, etc.) and ends up being an incomplete list for a large number of years (I sampled the most recent ~5 years and the oldest ~5 years and several major manufacturers are missing) as well as model of cars being incomplete for at least a few makes from those years as well.
The UI really isn't a problem, it just comes down to the company having the coplete set of data, which really is down to them either creating this list themselves or paying someone for it. I'm not sure of the case in the US, but if an online part company like http://www.eurocarparts.com/ or http://www.gsfcarparts.com can do it them I don't see what the problem is.
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).