A nominations system in which vouching for a candidate is more likely to harm than help their chances of appointment [especially if one is sufficiently convinced of their competence to believe 10 other people will feel likewise] is palpably absurd.
Some Twitch streamer with a thousand followers would have little problem getting 50 nominations by snapping their fingers, regardless of their qualifications.
This being said, there's probably a better way.
(Not to mention how easily the system is gamed by a membership groups orchestrating nominations. Pick 10% of your membership and get the others to nominate them and you'll have a lot of people in the hat. To be sure these candidates will be in the lottery, they'll want to select people who aren't well respected outside the group....)