MIT is not copyleft. The copyright notice must be included for those incorporated elements, but other downstream code it remains part of can be licensed however it wants.
AGPL and GPL are, on the other hand, as you describe.
AGPL and GPL are, on the other hand, as you describe.
You also could not legally remove the MIT license from those files and distribute with all rights reserved. My original granting of permission to modify and redistribute continues downstream.