"because it isn't stainless"
By your definition anything not stainless is carbon steel. And it really isn't so is it. Since in this thread we went on about to avoid overgeneralization about axes and their qualitities it really confuses things further by referring steels and their properties your way.
Yes, of course that kind of definition is incorrect. But it isn't my definition. A lot of people use the term that way, for clarity or simply because they don't know the difference. And that's what I meant. Often people talk of carbon steel and stainless steel, and bunch tool steels in with carbon steel. That's how a lot of folks use those words, even though it is scientifically incorrect. Now, when you quoted that post of mine and said something about it was "very incorrect", I had a hard time understanding what you meant. Because, you know, it's obvious that a) a lot of folks call all non-stainless steel carbon steel even though it's technically improper usage of the terms, and b) I thought my post pretty clearly showed that I myself understand that not all non-stainless steels are carbon steels, since I mentioned tool steels in my post. So, I rather stupidly thought that maybe you were somehow trying to say it's incorrect that a lot of folks use the word carbon steel to describe all non-stainless steel. I'm easily confused sometimes.
As an example, you could browse around this Wilderness forum and see how many times O-1 is mentioned, and note whether it's called a carbon steel or tool steel. I'd bet that it is more often called carbon steel than tool steel, even though it technically isn't carbon steel. Even knife makers tend to call it a carbon steel...
Now, personally, yes, I do know O-1 isn't a carbon steel. If I didn't know that, I probably wouldn't have written this: "O-1 is not a plain carbon steel, it is an alloy tool steel."
Perhaps that clarifies it a little. Now...
With your categorization of stainless and carbon steels the most important axe steel group is left out, tool steels and specifically shock steels. This is what the most demanding rescue and entry tools/axes are made of. So yes, I can think of many properties of steel that are enhanced when adding various elements, including ones that are used mainly in stainless steels. Including various effects that are produced by chrome.
Actually, no, it isn't left out - it just isn't mentioned as its own group of steels. Like I said, tool steels often get bunched in with carbon steels, and in 'my categorization' (which really isn't anything I've invented, or even anything I personally hold to, just something that a lot of folks use) that means that an axe that's made of "carbon steel" can actually be anything from 1055 to INFI, but not anything that's stainless.
I'm sure everyone can think of many properties of steel that are enhanced when adding various elements - if there weren't any such properties, I'm not sure elements would so often be added to steel even though it raises costs... But, you're not catching my drift. I questioned the performance advantage of using a stainless steel in an axe. I claim that there's no real performance benefit caused by making an axe out of stainless steel, except corrosion resistance, which is really rather pointless with axes. I would be willing to bet that your best axe isn't stainless, either, and that was my point. There are practically no good reasons to make a stainless axe, and that's why I find it hard to believe that Fiskars out of all makers would make their axes of stainless steel and then not tell anyone about it, still claiming their axes to be carbon steel...
Phew, that was a long post. Sorry about that.

But maybe it clarified where I stand a little. If it did that, I'm satisfied.