2FA has exactly one purpose: At some point in time a message is sent to a phone that is supposed to be in your possession, YOU (and nobody else) pulls that phone out of their pocket, and somehow acknowledge that you received that message. How owns the phone is irrelevant for this purpose, the only thing relevant is that you are in physical possession of the phone. Nothing is ever stored on your phone. There is no reason whatsoever why the company would ever want access to your phone.
People discuss whether you should use your private phone for work purposes. In this case, doing 2FA on my private phone saves me from having to carry two phones. The wear and tear on my phone and cost of data is less than any rounding error. So personally, for this purpose I would very much prefer using my own phone instead of having to use a second phone.
There are people who use a phone for significant amounts of work. Like having phone numbers of hundreds of customers and so on. That kind of thing should be done on a separate phone supplied by the company. Work emails have never been on any phone in my possession, private or work, but on a computer. But for 2FA and 2FA alone that's not a reason.
If you lose the 2FA phone, whether it's your private one or one supplied by the company makes no practical difference (assuming you would have lost that phone anyway, and it's probably more likely to lose a phone if you have two phones in your pocket instead of one). Having a second phone just to avoid interruptions when your personal phone breaks is not worth it. And if you want a works phone for this person only then at the time your private phone breaks, your work phone will be somewhere in a drawer and you can't remember where, you won't know where the charger is, and so on.