The first two stickies in the advanced topics section has pretty much all of the juicy ATS you could want, I don't think I've even been through most of it myself.
Could it replace the need for a protein skimmer? Sure. Does it have it shares of pros/cons? Absolutely, but then again what doesn't.
Cost is all relative when you really look at it. A ATS has an initial low(er) setup cost if your good with diy/ have the tools, and even some extra materials. You'll still have to power it with a light and it'll probably be in a sump, so if you don't have a sump already factor that in. Another part to factor in is that carbon may need to be ran in order to combat "yellowing" of the water. This may or may not be a an issue, but it could be an added cost never the less.
A protein skimmer is usually an initial investment but then it just takes electricity to keep it up and going. Plan on something along the lines of $200 initial investment, 2 week break in period, and the rest is just letting it do its thing.
For many nano's simple water changes is an easy cost effective solution without a skimmer or ats. Additional pros include not having to dose (depends on how much the corals tap the stuff), easy, and no real initial cost. Con is salt/water cost money, and plan on actually doing the water changes. I would say this works better on my 16gal, but not so much on 30gal, from experience. Others may be different.
Even a refugium may provide enough nutrient export. Macros you may find may not be as touch as setting up an efficient ATS. AIO nanos like the nano/bio cubes have this built in.
If it were me.. I'd probably go with a refugium or a skimmer for a nano than a ATS for a nano. Space tends to be limited for nanos. Also an ATS can be kind of finicky, which may be discouraging especially if your new to the hobby. Refugiums and skimmers are two good options that are more "plug and play". Just my 2cents.