I am not saying do not have the ability to authenticate to the app using 2FA, I am just questioning why build another 2FA code inside the app if you can use something like Google Authenticator. It just adds another layer of complexity that you need to ensure is secure. Building the 2FA code generator inside the app adds it to the same channel and it is best if 2FA codes are generated out of band.
I dont think there is any harm in integrating 2FA code inside the app, you need to have everything indigenous why rely on others? We dont know what Google policy will be tomorrow so better keep 2FA factor to yourself this will give confidence to your clients.