If you declare your beta “open” but require a beta key and:
Q: Where can I get a beta key?
A: Open beta keys are included in all pre-order boxes, and are given out by selected partners. Check back later for the list of partners that are giving out beta access.
then either you are unfamiliar with the term “open beta” or you are intentionally using terms deceptively. Neither inspires long-term trust for running a complex software project.
I’m saving up my snark about how long “paid beta” will run past release.