Radio transmissions are far from perfect. An antenna broadcasts in a variety of directions (some are designed to radiate in specific patterns, but they never radiate 100% in one direction), so you end up with transmissions going all over the room. Lots of materials reflect radio waves, so you get what's called "scatter." That means that the receiver will pick up both the intended signal as well as reflections from around the room. Even with error correction, scatter can be a pain.
Next, you have to deal with radio transmissions from others. The radio spectrum is crowded and band allocations can get contentious. Some bands are shared and some bands are for the use of multiple people at the same time. That can generally work a lot of the time, but you do not want to start picking up others' transmissions by accident. Like scatter, receiving others' broadcasts can be a problem.
Another reason is that you do not necessarily want a huge amount of RF around you. Wi-Fi, and all other radio transmissions involve RF. It can lead to long term problems, so I always try to minimize my RF exposure.
You can also get interference from other things, too. Switching power supplies, fluorescent lights, AC motors, dimmer switches, etc. all can throw off broad spectrum noise that can get in the way.
Adding radio transmitters and receivers to every piece of gear would increase the cos and complexity of items. Because things in a power supply can throw off RFI (diodes, for instance, can be noisy) you'd have to isolate the radio bits from the rest of the device carefully. Install it wrong and it'll pick up noise from within itself.
As for complexity, you'd then have another entire system to troubleahoot and repair if something goes wrong. That would just add to the cost.
So while this could be done, it's impractical for a number of reasons. I would stick with cables just for the simplicity. That's the same reason I run tubes - the circuits are much simpler and I want to keep the amount of components that touch the signal to a bare minimum. Everything the signal passes through changes it, so I want the fewest components.
Finally, the "problems" with cables are grossly overstated. I don't want to launch that debate, but consider that cable differences cannot be measured with standard test equipment. We can all agree on that. Further, no one has ever passed a blind cable test. You can argue test methodology, of course, but the lack of results from standard test equipment strongly indicates that the only difference between cables is a psychological one.