Later when enemies have more attacks and dish out enough damage to kill and not just down, the problem will be a new one. The nice unconscious buffer 5e has that is meant to save PCs from dying no longer works. Cheap resurrections are pretty lame from a narrative point of view so I really like that the unconscious state exists to protect the PCs from dying all the time.
Another problem is the AI that keeps attacking downed PCs. From a tactical point of view it makes no sense to waste attacks on unconscious targets when there are other enemies still trying to kill you. Unless of course you know reviving them to full combat capacity, albeit at 1hp, is just an easy action available to anyone and no one actually ever stays down. But that's the problem this whole thing started from. And it's much more metagamey than logical.