The marginal cost of sending a fax is, arguably, about one cent. (1.8c/min VOIP cost, 30 seconds to send, some electricity). Most faxes will be one page anyway, so the profit margin is a nice 10000%.
Finding a working fax machine if you don't have one sitting around all set up is a hassle on the order of 10 minutes to an hour, and likely to end up with a visit to a UPS/FedEx/Staples or the equivalent thereof, where they will charge you $1.50-$2 for the first page anyway.
Find a cheap old technology that people want to use infrequently and are therefore willing to pay a relatively large markup for convenience. Let's see... appointmentreminder already does voice calls for reminders, but how about automated, customized calls? Get a good speech synthesis app and let people send and schedule calls that read out whatever they want to type. That's probably worth a buck to people who only want to do it once, and then you can offer a subscription rate for frequent flyers.
EDIT: there’s definitely something to this thesis. In the case of faxes, they are an interface to older entities (government agencies and some businesses) and the unit cost for any individual to find a fax machine is relatively high. In addition, many fax services are venture funded and require subscriptions, when that isn’t really what many individuals need.