Actually I find that this method takes longer and does not save rehearsal time especially when people have not done their homework.
When you talk about
people who have not done their homework, do you mean the directors or the singers in the choir? If the members of the choir are also not committed to excellence, then you have an even more difficult situation to deal with. But if the choir members do have a desire to do better, maybe there can be ways to work it out. Ideally what should happen is that any choir members who are still feeling shaky about their part would feel comfortable saying, "I'm not sure I've got my part, I need to go over it a few more times." If they're hesitant to say that, maybe you can say it. Even if you're solid on the part yourself, if there are others who are not, you could say, "Can we go over the alto part a couple more times?" This might encourage others to be more vocal about getting the kind of teaching that they really need from their directors.
I believe that sticking with your choir and continuing to give your own best effort is the thing to do. It may inspire others, or maybe it will just be preparing you for whatever the Lord has for you to do next.
(Not wanting to be self-promoting, but if the directors are open to the idea, they can check out
ChoirParts.com and pick up individual practice tracks for a few songs, or make a custom order for a song they want to teach.)