I think that the quality of the steel and the variance in the heat treating added a lot to the low hardness in general. When you have to make room for error, you have to keep the RC down as it is far better to have the edge dent a little than to have it lose a huge piece through fracture.
Ideally you want the edge at the maximum hardness possible. This will give you the highest strength and thus allow the thinnest edge, this goes for all cutting tools not just axes. The problem with this is that once the hardness goes above a certain point the toughness gets lost rapidly and while the edge won't bend, it breaks fairly easily.
As Jimbo noted filing is very traditional, however right now I would question its need. How may people file their knives to sharpen them? If you remove this requirement, you can make axe heads much harder than normal. The problem here though, that axe edges are frequently rode quite near the limit of functional durablity and thus they get damaged a bit from time to time.
Now you can avoid this by leaving more metal there, but this directly lowers cutting ability. And when you are out in the sun and the flies are frequent, you want to spend the least amount of effort to get the job done, so you are without question going to have the edge as thin as possible. Thus you expect to do a little fixing every now an again for the knots and such, assuming you don't carry two axes, which is always a good idea.
The other point was that axes were not custom made, meaning the individual had them to his specs. This means that the edges had to be heavily reshaped to allow for the right geometry to suit the wood and the woodsman. Most general brands come close than others to NIB suitability , but nothing would be used as NIB. And of course files were the common method of heavy stock removal.
So the critical point is filing, if you do want it, then you can't go much beyond 57 RC and expect much shaping ability with a file. Some of the CPM shock alloys are promoted as having very high impact toughness even at ~60 RC. This extra hardness would allow for a thinner edge, how much so would be an interesting question.
-Cliff