I love my Milwaukee fuel impact gun but here's no replacement for air. Air is always there... batteries need to be charged. Plus as you've said, I spent more on my one battery impact set than I did on my entire compressor and 5 or 6 air tools. It's also about 3 times bigger than an air impact of the same power.
Air is always there; In the shop. Most of us do not carry around a compressor capable of running air tools. The battery tools shine in this respect. Our home shop is fully plumbed for air with about 8 different outlets and we run an Ingersoll-Rand semi-commercial compressor. Still, we rarely use our "mechanical" air tools anymore (impact guns or air ratchets). We routinely use air chisels, cut-off tools and sanders though. As far as weight goes, an air impact gun with the torque of a 18v Milwaukee isn't going to weigh a lot less and there's a hose connected to it. Batteries do die, that's why you have a spare (or two). I don't think I've ever ran any of my battery tools down prior to the spare battery being re-charged. If I did, I was working too hard and needed to take a break anyway, LOL.
I said to start with air tools are great and in some cases superior to the current crop of battery operated tools. Every shop should have a decent set, but, if you can afford it, the battery tools are much easier to work with in general. There are less expensive options than Milwaukee, DeWalt and Makita for the home shop. We have two 1/2" drive 24v Kobalt impact guns, a large one and a small one. The small one will handle pretty much anything a moderately priced air gun will and it's lighter, even with the big battery. Smaller too. It cost around $150-$200 depending on which battery you go with.
FWIW, I've also went to cordless nailers and staplers. I hate dealing with cords and hoses.