Except it looks like you don't need to use a new registration when you reinstall on a single piece of hardware - you only need to use one registration for each hardware setup.
As such, there is NO limit to the number of times you can install it on a single hardware platform.
In any case, since ED are managing the downloads and payment from their own servers, it should be reasonably easy to prove that you've actually bought the game. From there, it should be easy for ED to actually give you a new set of activations for your key
Whether they will actually do anything like that, nobody's saying.
In that case why ED dosent generate unique key which is binded to the guy who bought the game. In case of leak it will be easy to know who spread the copy. The pirate can only crack the game if he/she has the complete software. Knowing that your name is binded to the serial should discourage buyers from giving out the game for free to a "friend".
However in order to prevent any leak of serials all information should be stored on the computer which is not connected to the internet.