Speak for yourself, if my work gave me a phone like that for 2FA, it would be absolutely perfect because I wouldn't use it for anything but 2FA.
The hassle of carrying an extra device, charging it, storing it and taking care of it is exactly that: a hassle.
But, do note that we were talking about a phone for 2FA and you're talking about a phone for on-call. I'm too senior for on-call, but I need 2FA daily.