Any modern phone should be able to run a TOTP client. For my own FastMail account I have a TOTP client on my phone plus two Yubikeys, one I carry with me and one that I keep at home. We require all our staff use 2FA because emails from us get the magic green tick :)

So yeah, if I have my phone, I have a 2FA option already without SMS. I normally use the Yubikey because it's super easy.

How do you use a yubikey on your phone? Or did you mean in lieu of totp on your phone?

If you have a Yubikey NEO and a phone with NFC, you can store the TOTP secret on the Yubikey instead of the phone, and use the phone purely as a screen with a time source by opening Yubico Authenticator app and touching the Yubikey to it to generate codes.

For Fastmail I plug it into the USB port as usual (using an OTG cable). Last I checked that was still the only way to do it specifically for Fastmail, since they do not support NFC. For Lastpass though, using the Yubikey through NFC works great.