Someone has obviously found a way to do that, because the Dreamcast (which uses a modem) has had a recent revival with the Dream Pi project. (Woops... a few minutes too late for that revelation.)
I've been looking at this a little bit from a technology perspective, and while the client side is ubiquitous, the POTS side is not at all. Two modems wired back-to-back will not detect a dialtone, and so will not dial. You can use an AT command to disable detection, which will probably be sufficient for most people. Then you just need one side to answer and do whatever you dialed that computer to do. (E.g., start BBS software, or redirect network access via SLIP/PPP, etc.)
But, I've been trying to figure out how to become an internal SP, of sorts. As a network engineer, I started looking at old Cisco WIC modules and such. Lots of modems (which need POTS), and lots of cards to provide FXS ports, but they lack the DSP to act as a modem. They're meant to digitize the audio and hand it off as a SIP connection or similar. You could, in theory, have a SIP gateway with soft-DSP to speak modem, but I haven't found such a product yet. So, using an old Cisco 1U router to be a dial-up ISP in a box is probably not happening. But I think you could get two ATAs (or FXS ports) to connect two phone lines with modems on them, as long as you make sure the codecs are data-friendly. With an external modem attached to one, and via serial to the router, you could probably get the dial-up ISP thing to work.
The "big-guns" approach is to actually set up a PBX (of any size, from home office to telco), or if you want 56K support, get a digital modem bank and a T1 CSU and all that. Takes some space, some power, a considerable amount of telco prowess, but it creates real POTS service.
That's as far as I've gotten. It's a very back-burner project for me.