Heck, if you can collect the arrival times from the various airlines, you could send a confirmation message a few minutes after the plane lands. Checking in would be as simple as hitting reply.
That would require the traveler's flight information, which I wasn't assuming was something the rental software would have access to. However, if the customer wanted to offer it up ... sure!
Higher-end hotels have systems that do this kind of thing already, and there's no reason that rental car companies couldn't also.