It isn't necessary for your partner to follow you. Leading means to lead uke's motion by staying just ahead of it while you follow him.
As long as you stay ahead of uke's movement and mirror him, there can be no transference of power from him to you.
Some of this may just be semantics. "Leading" falls into my bag of bad language used to describe movement within aikido. I am also not a fan of "leading from behind." Ultimately, the spirit of leadership is to solicit a unified direction from another body. If your partner is not following your leadership, then you are not leading anything. Under such circumstances you are moving only yourself in a coincidental direction as another body. Once the coincidental movement changes direction, you have no authority to re-direct that movement. Often, we end up reinforcing our poor direction with either physical or verbal chastising. An example I think many of us experience is the "don't move there" lecture we receive when uke moves different from how nage desires [uke to move]. This does not qualify for my definition of leadership, much as the thought of army commanders standing behind soldiers and shooting those who retreat does not imply leadership.
You used an example of cart and horse. As I perceive that example, the driver's choice to sit behind the horse is irrelevant to the the fact the carrot must be presented in front of the horse and moved in the direction the driver desires the horse to move. Similarly, a driver using a whip to direct the horse must present the whip from behind to spur the horse forward. Both examples are not leadership, but rather aggravation.
Second, I have difficulty reconciling technique that splits movement. One of the things we practice as both uke and nage is moving with unity. If uke is doing her job, she would be pursing your center, not an extremity; if she got an extremity, she could transfer her whole body power into you because you are connected. The idea of baiting your partner is difficult to accomplish if your uke if not following a carrot, but rather following you. Imagine the carrot in your pocket as you sit behind the horse...
I think the concept of being ahead of you partner is not leadership. I think it is simply arriving to the best position first. If you partner is smart, that will change their position and you have adversely affected your partner's ability to control you. I do not understand why I need to use language that is relationship-oriented to describe what is individual movement; I believe the term "lead" brings with it the connotation of a role within a relationship (i.e. if I am a leader, then my partner must be a follower). To use this term and then not
describe the related role of your partner is confusing at best. To somewhat contradict your point, I argue that many people who train in this fashion do, in fact, need their partner to follow them. And that is not to take away from the success of training with a compliant uke who is helping nage learn how the movement takes place, but it is to point out a different training perspective.
To talk about my experience with Saotome sensei, he moves with balance. Your part in whatever he is doing is mostly irrelevant to preventing his movement. You move to points of safety from which you can press a new "attack". He often performs a silly little demo where you shake hands. This is one of the best exercises I have seen for introspectively looking at what "best" and "first" mean in a martial encounter. For me, this is the embodiment of irrimi.