Once any computer has ever had Windows 10 installed and activated on it then it will never ask for a product key again, but will pull the digital license down from Microsoft's servers. (Or at least as long as you don't change out the motherboard, as the digital license is directly tied to that piece of hardware.)
I have been told that if a machine came with Windows 10 Home, and you at some point upgraded to Pro, that a completely clean reinstall will go back to Home, but I've never had to do this so have never witnessed that reversion myself. I would have thought that the digital license tied to the motherboard would be updated on Microsoft's end to reflect whatever the "most recent edition" was that had been previously installed on a given machine.