If interrupted, the adventurers would get the benefits of a short rest (assuming that they have rested for at least an hour).
One reason to enforce the rule, I expect, is to counter the 5-minute-workday experience. If downtime is a luxury (and not something achieved trivially), players have an incentive to invest limited resources (spells, healing potions) wisely, and not blow them all on an encounter-by-encounter basis.
Obviously, not all table play that way, but it's a common enough trope that there may have been a desire to resist it. (and, since the DM controls all and can interpret what's written freely, it sonly resistance, and not prohibition.)
That's my sense.