Whatever, it's cool.
Mechanically, I'd say there's diminishing returns in extra attack rolls, but there's no reason fighters shouldn't be constantly slashing, archers shouldn't be constantly peppering the area, etc. The attack roll represents if one of your attempted hits actually gets through, not every attack you make, so I'm cool with 12 arrows per round represented with 1 attack roll just as I'm cool with 20 sword blows per round represented with 1 attack roll. Variable damage, in part, describes how many of those attacks land.
But it's cool, and it's something I should be able to imagine my D&D archer doing! And making multiple attack rolls has some utility (area effects, twin strikes, etc.) that might work for this.