One would think that pilots would use a frequency range that would be in the private (not public like Wifi 2.4/5.x Gh) range and thus never be overlapped.
What am I missing?
So there is a few reasons.
Flying is serious business. You don't want to take any risks having your metal box carrying a few hundred people fall down. You really do not.
Aircrafts are also pretty complex, and the parts, electronics, engines, wires and so on are undergoing heavy testing and verification before you use that part to build an aircraft. This is quite unlike consumer devices such as mobile phones, which just have to pass the minimum government tests to be sold to common people.
As there's numerous different mobile phones, with all sorts of radios in them, it's too hard to test/verify that none of them interfers with any of the electronics your airplane has. (I'm sure you've heard the recognizable sounds in a nearby speaker on an incoming call/SMS on a GSM phone - these devices really do influence other electronic.)
The easy solution is to just ban them, and require them to be turned off, because even if the chance is ever so small, you don't want to risk your plane full of people to fall down.
Once that policy was in place, many many years ago, it takes a lot of inertia to change. No executive wants to be the one making the decision and a few days later learn that something quite bad happened.
Add in the bonus of not having passengers be annoyed at the neighbour chatting away at the phone, and the passengers being more attentive during takeoff/landing.
Sounds like an excellent reason to prohibit bringing untested electronic devices onboard in the first place.
The fact that such a prohibition is not in place means that the whole thing is just so much security theater.
The rules were there as a "better safe than sorry" measure, implemented at a time when most people didn't carry many electronic devices (way before cell phones became popular). The pilots have training to fly with multiple instrument failures, but even so you want to do what you can to reduce the risk of that happening.
RF interference can occur in a wide area of the spectrum, so it's not really possible to eliminate it just by changing frequencies. Even if you could, getting the aviation community to change their frequencies which are used all over the world in all airplanes and at all airports would be exceptionally expensive.