Corten can work in less aggressive environments, but it has been known to fail to provide the expected protection in places with more acidic rain than was expected. Salt water is really aggressive.
Hot dip galvanizing does work, and is common for small boats, dock fittings, and other smaller items. There are also likely sacrificial anodes on the ship made of zinc.
(1) Rust wouldn't go all the way through. Surface rust isn't a problem.
(2) You want high-quality armor; toughness is key. Steel composition should be primarily chosen for toughness-to-weight
(3) And cost, of course.
Stainless would have been expensive, and given little upside, and potentially a lot of downside in terms of less effective armor plating.
Obviously, modern ships are entirely different (much less armor, actually, instead relying on active defenses), but I assume there are sensible reasons for materials choices.
But modern ships generally don't have any amount of armor except against the smallest of gunfire. The idea being is that if someone gets close enough to shoot at you with a sizeable cannon you're already dead.
The Navy would love armor that can stand up to modern missiles, but it isn't really possible, and the compromises in costs and inside space mean it isn't worth it. Maybe someday we will find a new material that would work, but for now ships rely on not getting hit.
I'm sure it was a concern in WWII, and that they took all steps they could to preserve their vessels, but I'm also guessing that as long as they weren't rusting so fast as to become junk in three or five years, they were much more worried about surviving combat than rust.
What could go wrong?