I wouldn't say that one role does more work than the other, but courtesy turn and butterfly whirl are asymmetric and led by the person who backs up. The person that is backing up can easily apply a speed up pressure to control the speed of the turn. For the dancer that is going forward, it's hard to give a speed up pressure when your hand is behind the other person and that person is going backward. You can't pull because there is nothing to grip.

The above assumes that the common way to follow is start out slow and speed up to match the leader.

Allemandes are symmetric, both roles are identical, so the speed must negotiated. This works best when both dancers are good at timing.

"Pick up your partner/neighbor, star promenade, whirl" is my call.