Because it takes a wizard!
even so, this spell is kind of underwhelming IMO, i might actually consider using it if the fire damage from each shot was persistent and had to be extinguished like alchemist's fire.like is the answer to far too many other things martials should have, i think the answer is 'there's a spell for that'
FLAME ARROWS:
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It's something I notice any time I play an archer and run into creatures that are resistant to piercing damage or who have vulnerabilities/special effects with fire. Getting access to firebolt is super easy, but if you don't want to fumble around with oil or alchemist's fire (which are improvised weapons in 5e, making them even less viable), you have no solution outside of magic. And it's almost always been like this (save for 3e, which had fairly robust alchemical items). I asked my DM about fire arrows, and even offered him that YouTube short to explain what I was talking about, and he might let us make a few during downtime, but the idea that something like this isn't standard equipment strikes me as insane.As others have said, flame arrows are not particularly useful against individual opponents, they're used for setting objects on fire. On the other hand I made a flametongue bow that adds 1d6 fire damage to any arrow it shoots because I'm not overly concerned about real world logic.
If you don't want a magic bow the real issue is to me that we already have alchemist fire that sells for 50 GP per flask. I could see adding alchemist fire arrows but considering how much more useful they'd be I'd also make them more expensive. So 75 GP, add 1d4 fire and dex save or start burning (continue taking 1d4 damage until you take an action to put it out)?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.