Athen democracy did have a system where you had to consent to standing in the process. I mean isn't that necessary? You only stand if you want to stand.
Also it's not being a leech, one of the biggest success of their democracy was to ensure people working for government get a salary. Without a paid incentive I think plenty of people would just not participate in it at all.
My upper estimate is half of the dau might want to participate, realistically, I think number could be as low as 30 or 20%