But the rest of the kids need to atleast recover. Sure, the Adult can do horrible things to Madoka if left to her devices for too long, but if we rush in, the Emerald City itself will do horrible things to us because we aren't prepared enough.
That logic doesn't work, if we gice the Adult more time, she will be even more prepared for us, and we also will have Madoka that suffered from whatever the Adult wants to do.
Plus, you really think Homura won't ressent us if we don't go to save Madoka with her right now?
She can be carried, her timestop is perfectly able to help us without her needing to move, and I absolutely and utterly refuse to let Madoka become the subject of anything the Adult concoct just because we decided she was too scary.
Think like the Adult, what would she expect? She's patient, she doesn't care what happens to others, she doesn't like taking risks.
Not going now is doing what she wants, what she expects, we have a better chance to take her by surprise by going now, and that is important.
The librarians can't leave the library, so that means no reinforcements from them anyway, Roland's reaction to taking Argalia in is going to lose us time, Homura's is going to try and go alone if we're not careful knowing her, doesn't matter that she doesn't have legs, Sayaka will also protest given her heroic nature, as will Mami, this is her friend that was taken there, taken by a monster that we know is a sadist mad scientist.
Taking them to the library will 100% appear as if we are going *hard woman making hard decision* to our children right now, and given the stakes, I would agree with them.
Edit:
Plus, what do you think our stop at the library is going to give us we don't have right now? A little time for the girls to calm down? They will not calm down with their friend in this situation. Time to heal for them? If we take enough time for that, we are letting the Adult prepare whatever horrible fate she has for Madoka in peace, plus all he traps she will do knowing we will come knocking on her door.
Think, the Adult had to act fast to attack us right now due to something we did, do you think giving her time to prepare is good when we may well actually catch her with her pants down if we attack now? The risks of not going far outweigh the risks of going IMO, by several orders of magnitude.
Edit2:
Honestly speaking, there's a reason we voted to have the girls rest before going for an assault.
The main reason for that was to allow them to enjoy the day and stabilize their mental state, letting them wait while we prepare while their friend is in the Adult's hands is likely to have the opposite effect.