If you are not willing to use google or microsoft authenticator app why not lead the industry with your own authenticator application which requires use of the encryption key to set up? Improve security by requiring the axcrypt app on the PC or Mac has access to location services and the axcrypt authenticator app has access to location services on the phone. If both devices are not in the same location, authentication via authenticator app would be blocked.
I can understand users desire to have an authenticator app option because the users are still exposed to other security risks if they are storing their encryption key in third party password managers or some form of cold storage. A authenticator app created by axcrypt would allow users to store encryption keys in more secure cold storage solutions. The location services managed by axcrypt could allow axcrpyt to better understand the location and device tendencies of it’s users so that over time, it would be able to increase the security of access via authenticator app.
Granted, this would block use of the authenticator app when location services aren’t available but users would still have the encryption key for those situations.