I would assume it's due to balance issues. There's a big difference between having to be out of combat to refresh the buff as opposed to having to be out of combat vs. champions.
If they changed it so that you only had to be out of combat with champions, it becomes easier to have access to Hail of Blades for trading and there are fewer windows of weakness for the enemies to take advantage of.
With the way it works currently, it also means you might have more difficulty with wave management because you have to make a choice between pushing the wave vs. holding off to wait for the the buff to refresh.
I'm not here to argue what the refresh mechanic should be. However, arguments about how things should change must always revolve around balance. Your initial point applies logic, but with no context of balance implications.
As a final minor note, Hail of Blades might only proc on champions, but you can still utilize the attack speed to hit minions. I bring this up simply since we could discuss/decide what 'works' means in your title for the sake of your argument.