In reallity, gas length is all about 5-7" from the muzzle. That sets the optimum timing.
What happened with "carbine" gas is it was carried over from the M4 and it's 14.5" issue barrel. Even that was optimized to work down to 10" barrels. Once the M4gery market got cranked up, the only way to meet the typical buyers impulse purchasing was to make the barrel length meet the NFA 16" minimum. Most buyers aren't waiting months for an SBR tax stamp.
Carbine gas on 16" isn't best, it's too early, with high gas pressures, excessive bolt carrier speeds, much higher blowback into the action, all due to the early opening of the bolt. It might be milspec, but the industry didn't care for it. They invented "midlength," which put the timing back to the correct point in the gas curve. And footed the cost of midlength handguards.
Some say carbine runs fine, the industry went to a lot of effort and expense to change it, and Uncle Sam wasn't picking up the tab. To me, that means it was saving them money, compared to carbine. Apparently the feedback was hitting the bottom line.
Midlength is correct, and runs better on 16", just as intermediate does better than rifle on 18". AR's don't have an automatically adjusting, expensive valve like semi auto loading shotguns that are forced to fire light bird loads thru magnum goose. They were set up to shoot spec military full power ammo, and there's no wide variety of loads issued. One or two are about it. So, the gas system is set up simple, no complicated valves, and runs reliably so. It's the civilian shooter running low powered import fodder that creates a CS problem. Strangely enough, it runs fine on carbine - less gas works better - but isn't so good on rifle - not enough gas to move things reliably.
Stick to full power ammo with the correct gas, things work, and accept that cheap ammo is just that, not the proper load, a get by.