Why does Windows process all NTFS child objects when changing a parent’s ACL?

Any child object that is configured to inherit it’s permissions from the parent object will need to be processed. Explicitly defined permissions on the child objects are not affected.

The option, “Replace permissions on all child objects,” will not only propagate the permissions to all child objects but it will also remove and replace any explicitly defined permissions on all child objects.

In Windows file permissions are not dynamically inherited. That is, when an attempt is made to open a file Windows only looks at the ACL of that file and not at the ACLs of the directories in the tree containing the file. That means when you change the ACL of a directory Windows has to immediately update the permissions of all files and subdirectories within the affected directory.

In Windows the inherit setting in an ACL does not indicate any form of dynamic inheritance. It is just a flag to indicate that when a parent directory's ACL is modified all files and subdirectories in the tree that have the inherit flag set must also be updated.

Those of us old enough to remember Novell NetWare will remember this was one of the big differences from NetWare because in NetWare inheritance of permissions is (was?) dynamic. There was much debate at the time about which approach was better, though history has rendered the issue moot. Dynamic ACLs require the OS to check the ACLs of every parent directory at the time an attempt is made to open the file, but changing ACLs is quick. In Windows opening file requires only a single ACL to be checked, but as you've found it means changing a directory ACL can be slow.

By default, child folders inherit permissions from the parent folder. Assuming the default scope when you're adding/modifying permissions on the parent folder (this folder, subfolders and files) then all child folders will be updated to reflect the permissions change at the parent.

The checkbox you're referring to is a "one time" operation that will remove all explicitly defined permissions on all child folders and replace them with inheritable permissions from the parent and will re-enable permissions inheritance on the child folders.