Installing an MFA token in your phone is just using a convenient place to keep tokens, not an imposition on you.
Objecting to being asked to keep MFA tokens on your phone is like saying 'where am I supposed to keep this keycard to get into the building? In my own personal WALLET?'
2FA tokens these days broadly follow TOTP and HOTP standards, meaning you can use any token manager you like to handle them. The iOS password manager even has inbuilt 2FA token support now. You shouldn’t have to install software just for managing corporate 2FA tokens any more than you need to buy a proprietary keyring to hold your desk drawer key.
Objecting to being asked to keep MFA tokens on your phone is like saying 'where am I supposed to keep this keycard to get into the building? In my own personal WALLET?'