Looking at the subject heading I think the obvious answer is that players want to win and feel like the site is not rigged. Although this is tough as a high percentage of online poker players are losing players. Whether the sites are rigged or not is not even significant to many of my players. I know at least 30 guys personally that deposit $50 after $50 who never have cashed out even once…………………yes it’s very sad but most of these guys are playing for entertainment and not grinding out a living.
I have honestly only met a handful of people that can consistently make a living gambling online and playing poker every day.
To answer your original question, players just want to win and not continuosly get crushed by bad beats at one site.