At least in the US, there's two different rules relevant to in-flight cell phone use:
- 14 CFR 91.21 [1] - FAA rule prohibiting use of any electronics during air-carrier/instrument flight which the aircraft operator hasn't approved, in order to prevent interference with the avionics.
- 47 CFR 22.925 [2] - FCC rule prohibiting airborne use of cellular telephones specifically, in order to prevent phones from talking to too many towers at once and stressing the cellular network. (As altitude increases the radio horizon increases, so at altitude your phone can "see" significantly more towers. The cellular network is built on the principle that a phone can only see a small handful of towers at a time, enabling frequency reuse.) This rule technically only applies in the "Cellular Radiotelephone Service" band, which is one of several different bands a cellphone can use, and it's one of the older ones — but you have no idea which band your cellphone is using at any given time.
The FCC has talked about updating 47 CFR 22.925 and/or harmonizing the rules between cellular bands, but who knows if they'll ever get around to it. [3]
FWIW, as a private pilot, I have first-hand experience with interference when somebody forgot to switch their cell phone off. It was difficult to hear ATC over the "click-click-BUZZ" of GSM interference through the headset. Granted, this was a small airplane, so passengers were much closer to the avionics... but it's not just a hypothetical.
Cell phones tend not to work very well (if at all) above about 5,000 feet anyway, since cell tower antennas are directional and pointed towards the ground.
[1]: https://www.ecfr.gov/current/title-14/chapter-I/subchapter-F...
[2]: https://www.ecfr.gov/current/title-47/chapter-I/subchapter-B...
[3]: https://docs.fcc.gov/public/attachments/FCC-04-288A1.pdf