12.5 is about the strongest winch I have seen from reputable manufacturers. I have seen a 13k winch on Amazon from China but wouldn't use it. I feel like 12.5 is fine. Jeep even sells a 8K factory option winch on a 5k+ lb vehicle. Not that I agree with that, I will get a 10K for my Jeep and have a 10K on the other Jeep.
Synthetic line is superior in almost all respects and no rope dampener is really needed, it just drops if it breaks.
In a perfect world, yes synthetic line *should* fall straight down. But doesn't always happen. Warn still recommends using a winch damper on Synthetic line. Its cheap insurance, and synthetic line snapback is a real thing.
The thing to remember about winch ratings and factory winches, is the OEMs try to spend as little money on these things as possible. And sure, they're fine for just the vehicle weight, but now add passengers and gear and you quickly get very close to the rating. For example, the GVWR on a AT4X HD is nearly 11K lbs, now add some extra resistance from mud, rocks, etc. and you very quickly exceed the rating.
Not saying it will 100% be an issue, but yes there are not many companies that make winches over 12.5K lbs, which is probably why the GM option is 12.5K. I know there are some companies (sherpa or superwinch for example) that make very high rated winches.