I've seen fire arrows used in person, (They have a viking festival in Yorvic, and they used to have a boat burning with a effigy of a dead king before health a safety put an end to it), and there is some written and artistic evidence of them, but they were very specialised (and expensive) arrow tips. You're right though that the flame would go it if the bow is fully drawn and loosed at full speed, so I can only see their use being in ceremonial (boat burnings for instance) or sieges of wooden fortifications where the goal is to set fire to things, not kill targets and you cant use the full tension of the bow and keep the flame alive.

I like shadiversity, but I struggle with his stuff occasionally. Hes a very eager amateur, and gets a lot wrong, not as much as he gets right, but theres obvious gaps in his knowledge.