I don't feel like it's cheating, but I do feel like motivation for others to join such a party once it's near full might be lower than one going by luck of the roll. Lots of people are likely to ditch once they get what they want, leaving the last few people to join out of luck unless the party leader continuously brings new people in, but it has to stop eventually, which means eventually the latest players to join will be SOL. Ideally the party intention from the start would be that no one leaves until everyone has one, but some people are greedy/dishonest, and for others life simply happens and they have to leave.
At least with rolling, everyone has an equal chance at each whistle, so even if the party disbands before everyone has it, they've had at least one solid chance at it (or at least a chance to have a chance at it assuming it doesn't drop on the last run ;p)