So what if one day we no longer need a router or modem for internet and instead we connect via tethering.
The phone is a modem (it converts changes in analog signal into changes in digital signal - it MOulates and DEModulates signals - that's what "modem"means). The tethering app is a router. It routes signals from a single external IP address to multiple internal IP addresses (and that's what a router is). Technically the only difference is that there's no Ethernet connection on the phone, but that could also be done (either wirelessly [there are "routers" now that can pick up the signal from your tethered connection and give you an Ethernet connection] or through the microUSB port).
If carriers gave truly unlimited data we could probably do away with a lot of cable and telephone internet connections. Except for one problem.
The bandwidth available to a cable company (looking from the cable company to the customers - the amount of bandwidth on the internet has nothing to do with how it's delivered) is limited only by the amount of glass we can produce. We may one day run out, but right now, the practical limit for any large cable company is probably in the yottabyte range or more. (10^11 bytes/second) Throw in a few more feet of fiber (diameter, not length) and you can multiply that by another 10. And so on. One company could probably provide enough bandwidth for every single person on the planet to be streaming a movie at the same time. (Which is more than the internet could handle.)
OTOH ... radio bandwidth is limited. It's increasing slowly (I'm more than old enough to remember when "communications" at 400MHz was limited to the distance between two rooftops of a university [anyone remember Brooklyn Poly?] as an experiment), but a couple of large fibers can carry more bandwidth than exists between DC and daylight. So the amount of data that can be carried by cellphone is limited by physics, and we can't "invent" new frequencies.
Right now there's probably enough bandwidth to accommodate the needs of most smaller cities, as far as using only LTE as a means of internet connection. But the amount of data (meaning bandwidth) being used is shooting up a lot faster than we can invent ways of getting around the physical limitations. So we're going to run out of radio bandwidth long before we run out of demand for it. (Even if we lowered power, so there wasa microcell every hundred feet, eventually we'd run out. And remember, cell towers, whether the huge ones you see along the interstate, or microcells mounted on telephone poles, are connected by - you guessed it - wire. So we can't completely do away with wire. The only thing we can do away with is the wire between your device and the cell delivering signal to it. And eventually we'll need a microcell in every house. Oh, that's called a router, except that it talks on 2.4GHz, not 850MHz.)
So there will always be a need for wired internet connections, until we discover (not invent) a new means of communications. Ansible, anyone? (If you don't understand the reference, see the movie or read Card's Ender's series.)