That's not what Unity is saying - they are saying reinstalls do not count. From their faq:
Does a reinstall of an app on the same device count towards the Unity Runtime Fee?
No, we are not going to charge a fee for reinstalls.
Does a reinstall of an app on the same device count towards the Unity Runtime Fee?
No, we are not going to charge a fee for reinstalls.
I agree what they are saying isn't workable, but that idea of install based fee could work, and would be better than a royalty for many.
This is the issue.