Example of terrible treatment by AAA
I'm really sorry to hear about your current situation, and then the insurance issue on top of it. It sounds like what happened was that AAA was taking advantage of a law common to many states that insurance carriers can non-renew policies within a certain period of time if they discover something they didn't know when they first wrote the policy. It's meant to give the carriers a way to deal with fraudulent applications.
When you're up to dealing with it, my suggestion would be to contact your state's attorney general or insurance commissioner, or both. Use words like "bad faith". The state DOJ and Department Of Insurance *love* the opportunity to stick up for the little guy against the big, mean insurance companies.
And because those independent agents get paid on commission, with presumably a larger commission when initially signing someone up rather then when they renew (no idea if that is actually true, but I'd think so), they'll be more than happy to shop you around when the 1st company you picked jacks up your rate after a year or 2. You continue to get lower rates and they continue to get a nice commission for signing you up to a new company, win-win as long as the rates continue to be less or comparable to online rates you could find yourself.
Depends on the carrier and their relationship with the agent, but generally speaking the commission from writing a policy new and renewing it are the same. Sometimes carriers will run special promos ("We'll give you an extra 5% commission on everything new through March!"), and sometimes they'll have extra compensation deals with the carrier ("If you're one of our top agents at the end of the year, we'll pay you an extra 1-2% commission on everything"), though that has been majorly controlled since the Spitzer cases (
https://en.wikipedia.org/wiki/Contingent_commissions).
The real reason an independent agent is happy to market your business for you is that it's way cheaper to keep an existing client than to find a new one, and they know that if you're asking them to shop you're probably looking at other options, too, like other agents or online. If the agent only makes a half effort and you find something way better, you're leaving, as well you should. And even if you have the cheapest price and you don't like your independent agent, you can move your business to another agent while keeping the same carrier. (This is called an "Agent Of Record Request". How it works is that while Agent 1 represents Carriers A, B and C, Agent 2 represents Carriers A, B, D and E. Let's say you're with Agent 1 and Carrier B. You like your coverage but don't like your agent's service. You can contact Agent 2 and say "Can I move my Carrier B policy to you?". They'll say "Sure!", put in the request with Carrier B, and probably also check Carriers D and E to see if they can get you a better deal. This would not work if you were with Carrier C, because Agent 2 doesn't represent them.)