It used to be possible to do this with a faxmodem; these days telephony is over IP, so there might be telco APIs for it. But, because it's a telco, that will be annoying and hidden.

UK: OFCOM are phasing out the fax support requirement https://www.ofcom.org.uk/phones-and-broadband/telecoms-infra...

(I slightly balked at the $5 initial price, but then realized: this is a desperation fee and I think for a lot of the users a clear fee for a clear one off service is the best deal. Anyone who wants to send 1,000 faxes will (a) be in the top 1% of fax users in their country if it's not Japan and (b) make their own arrangements. Also patio11's "charge more")

Software wise, if you have a PBX line (which the telco will change for) you can run Asterix and then https://www.asterisk.org/products/add-ons/fax-for-asterisk/ to send as many faxes as you like to the other person in your country with a fax machine.