To the first part, uh, what? The higher the chance of a random beneficial effect happening, the more "unfair" it is considered to be. You have it backwards.
No, you do. "Hax" is random chance. If Flamethrower burns you and it costs you the match, that's hax. If Will-O-Wisp burns you and it costs you the match, that's not hax. The fact that Will-O-Wisp has a much higher probability of burning (75% vs. 10%) does not make Will-O-Wisp "more unfair." The person with Will-O-Wisp dedicated a moveslot to picking up useful burns. The person with Flamethrower wanted an accurate, powerful, Fire-type, Special attack, and the burn is gravy.
The reason people dislike "hax items" like Quick Claw is exactly because they only occasionally do what they are supposed to do. If Quick Claw was like a perpetual Custap Berry, where you always go first within your priority bracket, it would be different. We would decide whether that power was acceptable or not and either ban the item or allow it. But when you are sweeping with Agiligross and your opponent has a Magcargo, and oops, looks like his Quick Claw went off and you died to his Lava Plume, it feels like you got robbed. This is precisely because there is no way you could plan for this. Magcargo goes first just 3/16 of the time, so the "correct" play is to assume that it will not. The fact that it randomly did, in the eyes of people who ban Quick Claw as a "hax item," makes your loss somehow less legitimate or skill-testing. The smaller the chance, the greater the "I got robbed" feeling.