Telephony is a cost center for most companies

This is the key here.

Since they transfer through a phone number, no data passes so they have no idea who you are

This really depends on the capabilities of the system and the willingness of the company to improve their CX.

For example, short info like customer name, ticket/account/order number, can easily be passed via text-to-speech, through the phone, to the agent on the line, before connecting the customer.