Umm.. no.
Two-factor authentication has two major requirements:
- What you know, and
- What you have.
What you know could be your password, or touchID that could be used to authenticate who you are. That satisfies #1.
For #2, they would need to send you something, like a code or a token in which you use in response to the challenge they give you asking for that response. That could be sent via email, or text, or any other means. Once you have that code/token, and you supply that to the app, you have satisfied #2.
That is device independent; I can still use my iPhone 6s to satisfy that for my bank's app or any app that requires 2FA. To say that you're forced to get a new device for 2FA is completely wrong.