While the final rule did not propose a pre-registration fee, it did indicate a fee may be proposed at a later time. On September 4, 2019, USCIS proposed a rule that would require H-1B petitioners (or their agents) to pay a $10 fee for each registration submitted for the H-1B lottery.
The registration fee rule is not yet final, but will likely become final in the near future. It is not yet clear if USCIS will have the electronic pre-registration system in place in time for the FY 2021 H-1B cap filing season, although it appears USCIS has every intention of having the system in place by April 2020.