Have you ever seen a quality (say Simpson) galvanized Class A pipe that's enclosed rust away?
(Real Life Disclosure - I work for a large construction company)...
If you want the shortest possible answer: Simpson uses hot-dip galvanization, which means it cannot possibly rust unless you puncture the pipe.
Oh boy. This opinion I think comes from a misunderstanding of metalurgy. The galvanized pipe is less likely to rust out than stainless. It's entirely counterintuitive. Galvanization works by dipping the steel in zinc, which chemically bonds it to the steel. The metals are hot enough there's actually a layer of steel-zinc co-mingled. Stainless steel is dipped in chrome (yes the same stuff on your car), but because of the properties of chrome its simply on there and not chemically bonded. What happens is light dings and scratches don't cause the chrome layer to be hurt, but when you get under the chrome layer is when the steel can rust and bubble up the chrome layer. This is very similar to the bubbling on a chromed car bumper. Normal wear and tear is called galling. For a chimney this chrome isn't pure chrome, it's usually chrome alloy of some kind. It's entirely serviceable. The empire state building, for example, is stainless. The portland arch is aslo stainless. They have to polish the empire state building because the chrome alloy doesn't deal with acid rain too well, but the portland arch they just let hang out. Like galvanization, big chimney pipe companies know wood smoke tends to be acidic and make their stainless steel to deal with it.
But, you're talking a process that takes 20 years. This is aggrevated in a low oxygen environment where the chrome is forced to give up oxygen it's absorbed and so in a hot, dry, airless environment (a lot like a chimney, actually) you can force the chrome to burn off or change it's PH enough to attack the steel. Short of a chimney fire, this isn't going to happen, but this is why chimney fires are so bad for chimneys. Inside the chimney doesn't matter as much because it's expected to be reasonably dry (no surface water). The outside of the chimney, not so much. This is why chimney pipe erosion usually starts at the top.
Galvanization is where things get weird. Galvanized chimneys from decent brands are almost all hot dip, which is what co-mingles the metals. You can actually electroplate it, and I think this is where the really cheap galvanized stuff got a bad name. Electroplating is worse than chroming because a piece might be galvanized, but the layer is so thin it's a joke. Furthermore you can subject metal to blackening where galvanization is actually semi porous and it's filled with oil. A little oil on a chimeny pipe is OK, it prevents it from getting dull in shipping. If it almost slips out of your hands or it has a sheen from the oil, it's too much and this is a sign that something was blackened rather than hot dipped. If you want an example of this, a lot of construction materials are actually blackened so that when you screw something together, the oil eventually wears off and the parts anneal themselves together from contact.
Now, knowing all that happy horse crap, put a 1ft section of pipe at the top of your chimney system and keep an eye on it. When the chimney starts to erode, just replace the 1ft pipe piece to keep the smoke away from the much more expensive 4ft ones.

EDIT: Before someone asks the obvious: Why is the inside of a chimney stainless rather than galvanized - The stainless surface is a lot, lot smoother which makes it easier to clean. The chrome process is expensive, which is why chrome pipes cost more. However, the chrome inside of a chimney isn't likely to die any time soon because there's nothing in there which could damage the chrome unless you're using a really, really aggressive brush.