In fact, it is possible for telephony providers to recognize fax signals, decode them themselves and just send the decoded bits over the connection, then re-gen

In fact, it is possible for telephony providers to recognize fax signals, decode them themselves and just send the decoded bits over the connection, then re-generate the fax sounds at the other end. See https://en.wikipedia.org/wiki/T.38 https://en.wikipedia.org/wiki/T.38 .