I think the good people at yubikey want to provide people with every possible form factor, for whatever is convenient for them.

If your organization issued you a yubikey, but you don’t like the form factor, I’m sure you could purchase your own and have them add it instead.

You can also use a USB extension cable, to add a bunch of flexibility between your yubi key and your computer, especially if you leave it always attached. That would remove the lever problem you mentioned