Aside from potential wear, the two main things that bother me is it will turn off even if I am just stopped for just a second (or less), and when it's really hot outside I want to keep the engine on. My previous Ford truck had this and I hated it. There was a way to jumper a couple wires to keep it off. It will turn back on when it thinks it needs to for the A/C, and the Ram does seem a little better about this than my Ford, but I still prefer full A/C when I'm stopped. And it's just annoying when you stop briefly when pulling into the garage or at a corner. It's quick but I don't want any delay when I have to pull out into traffic.
When I lived in a larger city they made a big deal out of it for emissions reasons. They claim cars use a lot of gas idling and supposedly this can improve your city mileage by up to 1 mpg; hard to believe it compares to the gas used for accelerating though. Granted you are getting 0 mpg but still. In the "old" days they used to make a big deal about how much gas it took when starting; with new cars it doesn't take much, but they still say it's better to leave it on if you aren't going to be stopped for more than 10 seconds. I've had it turn off and then turn on again before my rpms had even fallen to 0.
In Europe people were turning their cars off at lights manually when I lived there 40 years ago. The stoplights turn yellow briefly before green to give people a chance to turn them back on. If we had that here every light would be a drag race.
Yes there is a button but I just don't always remember, and even worse as I mentioned is sometimes it doesn't actually activate but I don't realize it. Most of the dealers I was looking at when I bought this ordered their trucks with it deleted, but the one I ultimately bought from did not.
It of course can't predict how long you are going to be stopped, and that is critical to whether it actually helps or not. I would be more amenable to it if the button function were reversed; if I were at a light and I knew it would be long, and the weather was mild, I would be happy to turn the engine off and let it restart automatically. But I don't like the constant cycling in normal driving.