If you really wanted that printer to be a dedicated fax machine, you could buy an Analog Telephone Adapter such as the
Grandstream HandyTone 701, and plug one side into the fax port of the printer and another into the Internets. Then you could buy a phone number from t38fax.com, generally via a
Free Trial, and configure the HandyTone to use it, and then you would actually receive faxes over the Internets on your own dedicated number.
The ATA "converts" traditional phone into the Internet-style SIP phone that all providers are using under the hood.
At t38fax.com it's $9/month for the phone number and channel, and 2.5 cents per minute for the faxing. But one gets a $25 credit with the Free Trial so that covers a lot of minutes.