Your phrasing is odd. 2FA devices do not support websites. Websites support 2FA options. The problem isn't 2FA devices, but services not supporting 2FA. U2F

Your phrasing is odd. 2FA devices do not support websites. Websites support 2FA options. The problem isn't 2FA devices, but services not supporting 2FA. U2F/FIDO are standard at this point and many tech-related services support them; certainly, effectively all 2FA devices support them. 2FA is redundant for unlocking physical devices. Access to the device itself is already a second factor. The point of 2FA is that someone MUST physically take something from you to gain access, which greatly limits attack vectors. If you use 2FA properly, the only thing you need to worry about for account security is whether you still have your 2FA key on you.