Why is it possible to "loop" a filesystem by mounting it to one of its folders?

When mounting a file system one add an extra layer for the system. The mount-point is an absolute path that normally hides the contents of the target. To have a closer look using stat can be of help. I.e:

First prepare a test case:

# mkdir /mnt/other
# echo hi > /mnt/other/hello.txt
# cat /mnt/other/hello.txt
hi
# stat -c %i /mnt/other
6424680

Then mount

# mount / /mnt/other
# cat /mnt/other/hello.txt
cat: cannot access '/mnt/other/hello.txt': No such file or directory
# stat -c %i /mnt/other
2
# stat -c %i /
2
# stat -c %i /mnt/other/mnt/other
6424680
# cat /mnt/other/mnt/other/hello.txt
hi

As you can see the inode for the mount-point changes from inode 6424680 to 2 (which is the inode for root directory¹). The contents of that directory is hidden as far as the mount point is concerned, but still present on the disk. It is a layer above the file-system.

¹ _{and parent to root, . and ..}

The path /mnt/other/mnt/other is not a mount-point and holds the original content for the inode of that directory. In your case it is empty, in my case it has one file; Though you could make it a mount point as well:

# mount / /mnt/other/mnt/other
# stat -c %i /mnt/other/mnt/other
2
# stat -c %i /mnt/other/mnt/other/mnt/other
6424680
# cat /mnt/other/mnt/other/mnt/other/hello.txt
hi

As for why, then why not. Unless it damages the system let the user do what ever they want. That's not saying one can not do things that damages the system albeit in this case the incentive to add a blocker is not present from what I can see. For what ever reason people might even want to create another view at a mount-point even of the root tree itself.

Further *nix systems have a single directory tree as opposed to e.g. Windows with drives that has letters A:, B:, C:, …. As per start of man mount:

All files accessible in a Unix system are arranged in one big tree, the file hierarchy, rooted at /. These files can be spread out over several devices. The mount command serves to attach the filesystem found on some device to the big file tree.