As far as including both "Good 'N Evil" and "Bring on the Men", the former serves to further Jekyll's quest and give him the inspiration for doing what he does (which is why it's never made sense to me to use Bring on the Men as a replacement for it) Bring on the Men was never a replacement for Good 'N' Evil. It was the reverse. And we've already had this explanation for Jekyll's motivation in both I Need to Know and the Board of Governor's scenes. Good 'N' Evil is just redundant, which is why it was cut after the world premiere in the first place. Probably because I Need to Know was replaced. There is really no point in using both songs. Bring on the Men is far more effective as a cabaret number and the second act really doesn't require another one. It just eats up time without adding anything substantive to the plot.
In other words, I Need to Know explains WHAT Jekyll wants, and Lost in the Darkness explains WHY he wants what he wants. Originally, Lost in the Darkness was explained by a short book scene with just a few lines which was all that was ever needed.
The songs that got cut like "I Need to Know" and "Girls of the Night" are great, but they don't forward the action, they tells us things that we already know and they make an already long show even longer. When it was just I Need to Know at the top of the show, it was actually the introduction to Jekyll's entire motivation, so it wasn't anything anyone heard before.
The purpose of "Good 'N Evil", narratively, is to give Jekyll the inspiration for developing the formula that he does (as I noted earlier). The Broadway book gives Jekyll a line about the song helping him. More specifically, helping him come to the realization that he has to use himself as a test subject, but it is not an element that the plot requires. Which really doesn't make sense given the lyrics. It's a cheeky song about the justification of choosing "evil" over "good", which is not what Jekyll is doing. It's a huge stretch to tie the song to his actions and shoehorning it into that scene never really worked.
Why does everyone like "Bring on the Men?" Yes, I feel "Good and Evil" is a bit on the nose but then we loose "No One Knows Who I Am," which is a great song and is a great introduction to Lucy's character. I haven't seen the incarnations since the Broadway production, but originally, it was just a stunning production number that added energy and brevity to the first act. No One Knows Who I Am worked beautifully as a follow-up to Girls of the Night, which added dimension to Lucy and the other girls. Not to mention its placement in the second act added balance to the use of Sympathy Tenderness in the first act.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian