How would MS Authenticator make it any better than TOTP?
To break TOTP, the attacker would need to:
a) be able to observe the initial exchange of the TOTP secrets. To do that, the attacker needs access to the victim's computer (on user level) at that specific time they set up TOTP. TOTP is a TOFU concept and thus not designed to protect against that. However, if the attacker controls the victim's computer at that time, the victim is screwed anyways even before setting up 2FA.
b) have access to the TOTP app's secret storage and to the victim's login credentials (e.g. by phishing). If the attacker can gain that level of access, they would also have access to the Microsoft Authenticator's secret storage, so there is no benefit of the Microsoft app.
On the other hand, Microsoft Authenticator is a very huge app (>100MB is huge for an authenticator app, Aegis is just 6MB, FreeOTP+ 11MB), i.e. it brings a large attack surface, especially by connecting to the internet.
I don't think Microsoft Authenticator brings security benefits over a clean and simple TOTP implementation.
I guess if there is WiFi, he won't even need a mobile data plan, so he could safe lots of money.