Of course, people did use modems extensively for ad hoc networking at the time. You'd call up your friend and transfer a file. You'd call up the local BBS and chat and transfer files.
Your question seems to be more, why didn't this develop into a more formalized system of always-on network links. Well, who's going to pay for all those phone lines?
Something like the Internet or another packet-switched network is predicated on (mostly) always-up links. Instead of calling your friend directly, you'd call a local access point who have another link to another site who have a link to another site who has a local link to your friend. Great.
Well, now the local BBS needs at least one always-on 24/7 phone link to another site. More than one link if it's more than just an end-point and is actually routing backbone traffic. Many of the necessary links would be a long distance phone call. Consider that long distance rates could be a dollar a minute back then, and I think you have much of your answer.
Protocols like UUCP met halfway. Sites would store-and-forward and connect a few times a day, often at night with cheaper long-distance rates. But a UUCP feed was complicated to set up, could involve a ridiculous amount of data (Usenet was megabytes a day even by the mid-80s if you wanted access to the whole thing), and was mostly reserved for fairly powerful minicomputers.
By the late 1980s, it in fact wasn't uncommon for networks of BBSes to be linked that way, and your email might make it across the country or even the globe in seconds. But by the time large networks of BBSes like FidoNet started formalizing their forwarding connections, and sometimes even having connections up 24/7, the Internet came around and everyone jumped on that.