I've been following the surge of interest and material on axes on the internet since about 2008. Even though it is not my main focus (material and official nomenclature from the industry), I can't recall ever seeing evidence in any form that manufacturers sold axes with different centerline shapes and hollows and marketed them as splitting, felling, or "general purpose" axes. The closest thing to that would have been, for example, comparing Kelly perfects, flint edge, and wood slasher axes. Mostly it was finish, but the wood slasher cedar I have is definitely not as concerted in it's geometric features. It's a big hunk of steel, with lots of extra material left on in places where this laymen thinks it ought to be removed.
I don't think it's a very reasonable approach to acquire only axes that are still in the same shape from the manufacturers-- assuming that, as you say, they came from the factory with their ideal proportions already (they didn't). A felling axe that was sharpened by a chump several times might well make a good splitting axe. And an axe that never had it's face filed down from the factory makes a great splitting axe. especially since a stock axe being put to used is probably a catalyst for a chump who never touched the edge, and it would require even more bluntening by means of a file to work a burr and subsequent edge onto it (which a splitting axe should have).
On the topic of capitalism and the axe industry, which I think is actually an interesting one, I also look at things differently. The manufacturers weren't the experts. When capitalism works well, the manufacturers interpret information through the market (This is the technical merit of capitalism, and the opposite point is probably the most compelling argument against socialism I've yet to hear, from Hayek). There were a million and one attempts from manufacturers to market superfluous, inexpensive, and inefficient designs. These only ever started to catch on when people stopped using axes. Roughly coinciding with the general abjection of the quality of people, thereby destroying what shred of merit capitalism had. Just how I see it. It's the responsibility of the consumer, in this example the old men who actually used their axes, to send a message to the manufacturer what they want in an axe. In a time where people did things themselves, idiosyncratically, and with different preferences abound, that message was not to produce homogenized "ideal" axes, but to sell something that could be shifted either way with a little bit of work, and be re purposed as it was worn (for example, blunted by means of hard use and sharpening, yielding a splitting axe after a long tenure as a cutting axe). I could be completely off base here, but like I said before, I have never come across or heard of any manufacturer doing what you elude to-- if they did, I should think that they would have made it known that their axes had "shallow centerlines" or some other equivalent term with the same or similar conveyance that meant their axes cut better. Most of the material that would roughly meet that criteria would fall into the realm of capitalistic drivel that was promptly rejected by the consumer (a beautiful part of capitalism).
Of course each and every axe needs to be assessed individually-- but the profiling of an efficient axe draws from so many different factors. I think the FS advice in "an axe to grind" is actually pretty moderate. The problem you bring attention to is real, but I don't think it is necessarily a problem that will arise from filing back as illustrated by Bernie. He doesn't file back all that far; like I said, it's fairly moderate. Peter Vido sharpens his axes to the old standard amongst the New Brunswick axmen. Read this excerpt here--
"During the early stages of my ax sharpening search, the local old timers were rather vague with advice. They plainly did not think of head/edge shaping in terms of specific angles; if I showed them one of my axes, they felt the bit between their thumb and first finger and (usually) declared it too thick here or there… Only one of them, Arnold Hanscomb, was explicit: he laid a file between the edge and the centre of the ax's eye and said but one word: "FLAT! " He fixed my gaze and repeated "Flat… then you will have an ax that cuts." ALL our axes back then failed that parameter, most of them miserably. Though I later tried to meet his specs, I too failed, mostly because it took a lot of time along with many good files to properly convert the worn and abused old axes we had collected, which had the cheeks too thick to allow for the file (or other straight edge) to lay 'flat' -- that is to contact at once the eye and (almost) the edge.
If you go and check your axes, I would wager that they too would likely "fail" this test. An axe filed that extensively has its centerline negated through filing very, very far up the face of the axe. An axe filed that way does penetrate and cut extremely well, and the release is not terribly difficult, because if it's done right, the context between the different geometric factors is still (usually) synergistic. The further you go up the face of the axe, generally speaking, the thicker it becomes. So whether an axe bites an inch deep, or 4 inches deep, if you know your stuff, a bulge further up the face of the axe that is filed in that manner (using the straight edge) is going to eventually become a factor as the axe penetrates deeper. That is going to open the cut, create a point contact, separate the fibers, and penetrate very deeply to boot-- assuming it's done right. Every axe is different, and plenty I'm sure do not respond well to this kind of filing. It's dependent also on the wood you're cutting, and whether it's green or dry, or frozen.
I'm not telling you that you are wrong, just sharing my experience and thoughts. I'd like to see pictures of the way you file your axes if you have time.
Both are useful methods. Using a grinder does require precautionary steps that aren't needed with manual methods, though. Even better if you can get your hands on a slow speed or manual wet grinder.
