I would presume it's because the chains get access to a HUGE member base and I would not be surprised if they got some sort of kick-back from AAA/CAA to offer preferred rates. AAA/CAA charge considerable member fees and this is a way for people to feel like they are getting value for being a member beyond the potential for roadside assistance. If you are a AAA/CAA member you get access to discounts on all kinds of things, hotels are just one of them.

It's usually a modest discount, rarely anywhere near as good as a negotiated Corp Rate, and as the OP suggested, the discount seems to be even less than what it was in the past with tighter restrictions.