Hi people -- I think that we are asking the right questions but not taking into account the evolution of things.
Even tho there were certainly some very strange things produced -- I tend to think largely by guys who were good engineers but hadn't a clue as to how/when cooking was done(call this catagory 'Quintessentially Male' -- eg. Waterman's initial 3-cup molds) -- my bias is that production is:
1) Primarily functionally oriented(esp. outside an Aristocratic, or other culturally formal setting -- eg. Host Makers, Japanese Ceremonial T-pots etc)
2) Optimized depending on the level/pressure of competition
3) With developmentally 'Form Following Function' -- but following it at a distance(things/fixes often getting complex before they have a 'catastrophe realignment', & get simpler(eg. the Griswold waffle hinge).
Initially the 3 legs on the CI pots were the minimal amount necessary to stabilize the vessel in a coal/wood hearth fire -- especially when even the burning 'ground' was likely to shift under the vessel.
As 'first growth' forest was supplanted by smaller sized wood, & the open & then fireplace hearth was superceeded by the wood/coal stove, the legs became progressively shorter, winding up as the 'nub' forms we are familiar with on some of the early transitional -- fireplace->stovetop -- cookpots.
In this, one of other selective values for the legs was to keep the pots from being 'tippy' due to the protruding bottom.sprue->gate casting mark. When these were originally 'snapped off', they often extended a fair bit below the pot -- but since these, esp. here in the 'frontier' US were just 'functional objects', no-one much cared/focussed on it.
One of the problems in even trying to grind these smaller, was that the protrusions were completely under the pot -- so the grinding had to be done 'blind', relying on familiarity(or possibly a mirror -- but have never heard of such being used). Of course, when the 'side gate' was later introduced, it was easy to see where & how far to grind off the 'gate', & the bottom feet became superfluous.
While awaiting for this, on the inside, as the stove/range 'oven' was developed -- around 1830 in the NE. area, but about 80 years earlier in the Pa. Dutch areas -- a large flat area became available to be used for baking -- which for larger, flatter pans also selected for another 'foot' being added to the vessel, but this time as a 'leveler' to keep the pan as a whole from being 'tippy', vs. something to just extend below the pot's bottom 'gate'.
On the outer, stovetop, however, with the advent of the 'stove lid'/'stove lid hole' -- around 1840 -- the pot was allowed more direct access to the heat that was circulating under the stovetop, and around the outside of the internal oven. To have the vestigial 'gate' legs keep the pot above the stove would have been counterproductive -- both in terms of wasted & inefficient heat re. the distance, and also in the 'spoiling' of the draft re. an open stovelid.
Some of the legs then initially just hung down in the stove lid hole -- whether or not the pot developed a 'pit bottom'; while others seem to have evolved into(as CB noted) what I call 'centering' tabs(in Troy's beautiful pan) -- & eventually, also 'rings' -- whether centric, or eccentric(even not associated with a 'pit bottom' -- to specifically 'center' the pot re. the hole, re. the stovetop(much as we make use of our limited 'Desktop' on the computer).
In evolution the predilection to sponsor change from what is already effectively 'at hand' is called 'preselection' -- a different use, with its own selective advantages/disadvantages -- being made from what is already available.
In this regard, the multiple tabs on the bottom of Roger's gorgeous pan could well be at once a 'selected' stabilizer for the 'tippy' gate, a 'preselected' 'leveler' for its use as a 'bake pan' on the flat surface of the internal oven, & a 'precursor' of what later developed into the 'heat ring', when the multiple, ineffective(as I believe Troy noted re the openings between them) peripheral tabs were finally united(although it should be noted that there were some absolutely huge diminishing rings -- usually for the 'mushroom' tops of eg. CI train-depot pot belly stoves, that could easily have accommodated the tabs on Roger's pan as 'centering' tabs -- the Q here being, how many pans were likely tailored for this specific niche? -- possibly some).
It should be remembered, that although there were some fireplace pots/pans that didn't have feet -- being either hung or placed on 'fireplace trivets' -- there was no need for either centering tabs, leveling(greater than 3) bake feet, or 'heat rings' until we get to the context of the stove.
Once here, even tho apparently similar, & similarly derived, the stovetop 'centering ring' does exactly the opposite of the 'heat ring' -- the former keeping the vessel in a specific place, & simultaneously, of necessity, creating a 'hot spot', & the 'heat ring' raising the pan up ~ 1/8" to effectively 'spread the heat'/create a 'heat pillow' -- so that most all of the pan is ~ evenly heated.
[NOT a 'smoke ring' to keep the chimney 'down draft' from blowing the smoke out into the room -- as easily done by keeping the pan flat over the hole; which if it were endemic meant that there was hardly any constant draft to stoke the fire]
Even here there were always some variations -- eg. some heat rings with deliberate perforations(eg. Lodge? like a mini-version of Rogers eg.) in the periphery, to purposefully 'waste' some of the heat -- possibly to keep the 'heat pillow' from stagnating, & preventing hotter updrafts from refreshing it)
But with the development of the 'positive draft' gas stove(vs. the 'negative draft wood/coal stove'), as the gas burner trivet rose above the level of the stovetop, there was no longer any reason for a 'heat ring' to 'even out the hot-spot' over the stovelid hole -- so the 'heat ring' generally disappeared -- except it didn't -- not in the large skillets. Why was that?
Another way to look at the 'heat ring' is that even tho we can think of it as stabilizing a 'heat pillow' under the entire skillet bottom above the stove lid hole -- in creating a larger area for the heat to fill than if the hole was 'capped' by the skillet sitting flat on top of it, it sponsors a relative 'vacuum'(the larger area), & then stabilizes it.
But once the gas burner is completely open at the sides, the entire room is effectively a heat 'vacuum' relative to the burner itself. Where the pan is small, this doesn't matter -- it gets its heat by direct contact from the rising gases from the burner. But as the pan gets bigger, the chance that turbulence due to the heat differential becomes likely to also bring relatively cold air into contact with various parts of the skillet bottom grows progressively larger. In this case the 'heat ring', small tho it is, probably acts to marginally contain the openly dispersing heat -- increasing the general heat density, & uniformity. It is here also acting as a relative 'container', but in a way, sort of the opposite of its containment on the wood/coal stovetop.
fwiw
