4e tried this, limiting longbows to 20/40 (or 100 to 200 feet). The problem was, historically English longbows could easily hit 100 to 200 yards, so it was a pretty hefty reduction of "realism" for the sake of game balance and making other tropes viable. It was nerfing Legolas so Gimli would be "balanced".
Adding an "aim" action might be one way to have balance. Slashing bow range when firing-on-the-run.
So you can make a snapshot at a close target at point blank range (within 60 feet) and then move. But if the target is farther away you need to stop an aim, which prevents movement (let's say within 200 feet). And any farther away and aiming is an action, as the arrow takes time to fly and you need to adjust for their movement during that time.
(Switching from bow to melee is easy, as you can hold the bow in one hand, and then draw a sword as your object interaction. Switching from melee to bow is harder as you need to drop that weapon.)