The discussion of the economics of what a dealer should charge is a waste of time. preaching, or whining, about it is not going to change it one iota. The solution is simple, if you don't like it, don't pay it. Find an indie mechanic, diy, or get an Acura as someone stated. To get any info from this thread requires skipping over a lot of those BS comments. But there is still some good info in this thread.
Back to the original issue, as I understand from the gems of actual info pertaining to the subject on this thread, registration appears to be just that. A recording of the event. The dealer may also clear faults but doing so is a separate event. It seems logical that operating with a dying battery may cause the recording of faults? As for the dead battery of the contributor from Tucson, my experience with living in the Sonoran Desert (Phx), is that the extreme weather kills batteries quickly. I thought the cold weather of the upper Midwest was hard on batteries, but it is nothing like the desert's extreme heat. I am glad my car's battery is not under the hood with the heat from the turbos. I learned here that my 335 has an AGM battery, but there appears to be conflicting info as to whether this is an advantage or disadvantage in the heat. My car passed its fourth BD in July so it will be interesting to see how long the battery lasts. The SLA battery in our 2004 Acura TL lasted just over four years. When a new battery is needed I will replace it with an AGM, from the dealer or otherwise. I may even register it. By the then I may have the tool to do so.
A couple of anecdotes of my own. I agree that my 335 is over engineered and over complicated, but it is SO MUCH MORE FUN than the TL, I plan to keep it as long as I can. I had to get my car towed to the tire shop when one of the run flats chose to no longer run. From what the tire guy says the run flats do not care for the heat either. And the tow truck driver regaled me with his experiences picking up big BMWs and Benzs with electronic emergency brakes. He said when those batteries fail, they lock the brakes. The tow truck has to drag it out of where it is parked and on to the truck.