Score one for the tree huggers. Fax machines waste ink. Ink cartridges don't grow on trees either. Fax machines are slow. And with a fax, you still have to wait for a printout.
Fax machines waste time.
In the time that it takes you to go to a fax machine, retrieve a fax, and then fax or call in a response, you could have answered a dozen emails. Fax machines waste space. The machines themselves are a waste of valuable office real estate. The paper that they generate is a real space waster as well. Faxes aren't secure.