Are there teams out there that are looking to hire a driver?

Nope. There are no teams that are all set up with a rally car, service truck, trailer, and a battalion of crew guys that are stuck in the garage saying that if only they had a driver, they could go rallying.

Since 99% of the time, the driver is the one paying the bills to go rallying, there's always a driver available.

There are a lot of great ways to get involved in rallying, such as crewing for a team or volunteering at an event, and hundreds of people do that each year, and then work their way up to driving their own rally car. But becoming a hired driver, without investing 10 years of your time and hundreds of thousands of dollars of your own is not an option.