Okay... I feel I need to put a bit of insight based on common sense and logic rather than historical precedent (I don't have the sources on me)... but it seems pretty well confirmed now that flaming arrows are indeed used. Those who argue seem to be completely missing the point of them (NPI).
No, not all archers will be using only flaming arrows all the time, because they are ineffective at killing their target (Again, lack of penetration, accuracy, and range). But their point isn't really to skewer the enemy (Though it's an added bonus if a few, but not too many, do). The purpose of a flaming arrow isn't to stab people from a distance like normal arrows: it's to transport the fire from point A to point B.
The biggest point anti-flaming arrow people seem to be missing is the purpose of mixed weapons and varied arrow types in the first place. There's a continuum for the type of arrow used, with range, accuracy, and penetrating power on one end, and the odds of setting great areas on fire on the other. Standard arrows are virtually incapable of setting anything on fire, but have good range and penetration. Burning rag arrows are also used at not-as-far range, to set the areas on fire, with the arrow tip doing little more than serving as an anchor to whatever it hits without bouncing off of.
The kicker is that if it does penetrate, it only goes in 1 inch and because it is on fire, it cauterizes (might be miss-spelled) the wound.
Cauterizing the wound isn't doing the shot guys a favor, and isn't true anyway. What a flaming arrow does do on the rare chance it penetrates and is still burning is it
BURNS, and radiates pain and system/flesh damage beyond the immediate impact point. It also disfigures, making it very terrifying.
I'm rambling... Short point is... Normal arrows are for killing people. Arrows on Fire are used for area denial and battlefield control. Both have a place on the battlefield, so both would likely be used whenever practical. In Tamriel, Khajiit will find a way to use them whenever possible.
Magic arrows should also be taken into consideration: They have all the advantages of a Hyperflamable arrow, while also having all the advantages of a standard arrow but one: Cost. So, they'd be rare, but at least a few deployed... I think they're comparable to modern grenade launchers.
EDIT: Also, I think we need something to discuss the effect Tamriel has on warfare... After all, those Imperial Battlemages aren't just for show, and I'm pretty sure in the case of a certain race of felines have their biology making them Min-Maxed soldiers shakes up the dynamic somewhere as well.