To address the “why”:
A user account, as defined by a username/password combination, can be used to access resources on the machine without logging in interactively on that machine. In a perfect world, you would only ever log in interactively on the machine using an account with restricted permissions, and when you needed to do “administraty” things, you would provide separate admin credentials at that time (sudo, runas, whatever your OS of choice supports).
Bonus question - what are the risks of having a weak password on a root user on a spare laptop on the same network as my main device that is used exclusively for web browsing?
If someone is able to compromise that root user on Machine A, then they may be able to leverage Machine A as a platform to attack any other devices on your network, or make Machine A into a zombie in their bot army to attack other targets anywhere, send spam, whatever malicious shenanigans they desire. (I know that’s pretty simplistic, there’s a whole lot of details left out, but that’s the gist of it.)
Also, nobody has yet mentioned the PIN option. I know that Windows machines (at least some of them, depending on configuration) allow you to configure a PIN for logon for local accounts. This PIN is only stored locally on the machine, and is not transmitted anywhere else. It’s basically a “shortcut” to the full password, and I think it can only be used for interactive logon.
While “Cisco Duo” is not listed here:
Trademarks are exactly how rules for naming things works.