While strictly true, that is not a very useful approach to take. By the same reasoning, _every_ operation is either O(1) or does not terminate, because a system with bounded memory has a bounded number of possible states.
I can see why it's especially tempting to make that jump in the case of O(log n), but that's just not the way this type of analysis is performed - a more conventional way of stating your point would be to say "yes, it's theoretically worse than O(1) but for practical purposes the constant factors matter far more".
I can see why it's especially tempting to make that jump in the case of O(log n), but that's just not the way this type of analysis is performed - a more conventional way of stating your point would be to say "yes, it's theoretically worse than O(1) but for practical purposes the constant factors matter far more".