I think most of them are sold at auction. From the owner's point of view, they make a large, immobile tax and legal liability disappear, providing a recepit for use as a tax deduction. From the charity's point of view, I expect they get a monthly check for allowing their name to be used by the reseller. A GAO study suggests that the charity receives a fairly tiny portion of the sale price, and a lot of the proceeds pay for billboards and other promotion. My e-mail confirmation came from "habitatforhumanity@arscars.com" and ARS makes grand promises to non-profits, but it's free money for the charity so I doubt they scrutinize the income very closely.Donated it to one of those charities? What do/did they do with donated cars exactly?
Most sources of funding for non-profits either take a lot of time away from the work they want to be doing (fund-raising events) or come with burdensome reporting requirements that are going to keep one or more employees tied up doing paperwork instead of what they signed up for (pretty much any government grant). If not seeing the bulk of the money from donated cars is the worst thing about doing car donations it's still a good arrangement.
I agree: everybody wins, but not everybody wins equally. I probably spend half my breath here arguing that such arrangements are good, or at least better than any plausible alternative.