More holes in a burner do not make a bigger flame
Why the spacing between flame ports decides how much of the released heat ever reaches the pan.
Adding ports to a gas burner, or opening the ones already there, does not increase the heat it produces, because the amount of fuel arriving is set upstream by the jet and the supply pressure and is entirely indifferent to how many openings that fuel eventually leaves through, so all the port pattern can change is the shape the heat is released in and how much of it lands on the thing being heated.
I spent a long time working through variants of one burner head in which the ports were made larger, more numerous, and rearranged in every combination I could generate, and the arrangement that put the most heat into the vessel above it was not the one with the most port area, nor the one with the most ports, but one with fewer flames spaced further apart than the design it replaced.
Why crowded flames grow taller
A single flame sitting on a single port draws the rest of the air it needs from the room around it, since the air entrained upstream is deliberately less than complete combustion requires, and that second helping of air arrives sideways through the flame's own surface. This is the part of the arrangement that the port pattern controls, because a flame surrounded by open space is surrounded by air, whereas a flame with neighbours on both sides is competing with them for the same supply and is partly shielded from it by their bodies.
Push the ports closer together and the flames begin to behave as one. The reaction, unable to find enough oxygen at the sides, continues further up before it finishes, so the combined flame grows taller than any of the individual flames it was assembled from, and the region where fuel is still looking for air extends up with it. Since a taller flame on the same burner is very often reaching past the vessel rather than into it, the visible result of crowding the ports is a bigger flame that delivers less heat where it is wanted, and if the vessel sits low enough to interrupt the reaction before it has finished, the quenched flame leaves carbon monoxide and soot behind rather than the completed products it would otherwise have made.
Spread the ports too far apart and a different failure appears, because flames on a burner light and hold one another. A port whose neighbours are out of reach has to survive on its own against the mixture rushing past it, and a burner spaced that generously becomes hard to light across its whole face and prone to losing individual flames when a draught crosses it or the gas is turned down.
Birthday candles and a shower head
Candles on a cake behave the same way and demonstrate both halves of it in about ten seconds. A candle standing on its own burns with a clean tapered flame that ends where the fuel runs out of things to react with, while a handful of candles pushed together into a tight bunch produce one tall, restless, sooty flame that is markedly harder to blow out and leaves a mark on the ceiling that a single candle never manages. Nothing about the wax has changed and no more fuel is being supplied per candle. The inner candles simply cannot reach the air, so their reaction finishes higher up, and the flames merge into one column that carries unburnt material further before it is consumed.
The other half of the idea is a shower head, which is a fixed supply of water divided among a set of holes, and drilling more holes into it does not produce more water, since the pipe behind it delivers what it delivers and the only change is that each jet weakens. A burner head is the same object with a different fluid in it, and the temptation to read added port area as added capacity comes from confusing the thing that meters the flow, which is the jet, with the thing that distributes it, which is the pattern of holes.
A speed window only a few times wide
The mixture leaves each port at a speed that has to sit inside a surprisingly narrow window, since it must stay comfortably above the speed at which the flame can travel back down into the port and comfortably below the speed at which it tears the flame off the port altogether, and the upper limit is only a few times the lower one. Total port area is what places a burner inside that window, because the same fuel flow divided among twice as many openings leaves each of them at roughly half the speed. Doubling the port area of a burner that started in the middle of that window can leave it near the bottom edge, so a designer who adds ports in the hope of more heat is walking a premixed flame towards flashback, the point where it can no longer sit on the burner at all.
Flame height and port shape are separate questions
None of this settles how far the flames should sit below the vessel, which is a separate question that can undo a good port pattern completely, since a burner spaced correctly and then placed too close to a cold surface has its flames interrupted before they have finished. Nor does it say anything about port shape, and a slot, a round hole and a ring of small holes of the same total area do not behave identically even when spaced identically.
Judging a burner head by the pan
The useful way to think about a burner head is that the jet decides how much heat there is and the port pattern decides where that heat goes, which means the pattern is judged on how much of the released heat crosses into the vessel, however unimpressive the flames that do it. That reframing is what makes the awkward results legible, since a burner producing shorter, quieter, less dramatic flames while putting more heat into the pan is doing exactly what it should, while a generously ported head throwing up a tall soft flame is very often losing heat past the sides of the vessel and making carbon monoxide as it goes.
Where I had this wrong
I treated the port pattern as a way of setting how much heat came out, and I began by adding area whenever more heat was wanted, which produced flames that looked like progress and measured like the opposite. What replaced that belief is the recognition that the fuel rate had already been fixed before the mixture ever reached the head, so every arrangement I was comparing was releasing the same heat as every other one and the only thing under my control was how much of it arrived where it was supposed to. The variants that eventually performed best were the ones I would have rejected on sight at the start, and the cost of learning it that way was most of the study.