Two-factor authentication is an account setting, not a device setting. Once turned on, it can’t be turned off. For a growing number a features two-factor authentication is a requirement.
Signing in with two-factor authentication on older hardware is a bit special, but works fine, and shouldn’t have to be done that often.
If you have an Apple TV (2nd or 3rd generation) and two-factor authentication for your Apple ID, then you may be asked to type your password followed by the six-digit verification code directly into the password field. Additionally, there is a time limit, after which the code becomes invalid.
Try this: First enter the characters of your password (do not submit yet), then manually request a new verification code, then append that code to the password (no spaces or other separating characters), and then submit. That should help you get passed the time limit.