Why not more wireless connections?

Wireless definitely has the advantage of convenience.  For me personally it's really more about reliability. I have suffered in one way or another through many versions of wifi, sometimes in very congested areas sometimes not.  

Devices overheat for no apparent reason and wifi drops, your neighbors new Comcastg router just added 8 new wifi signals on your band and is crowding you out.... that's my biggest beef with it. 

The other one is EMI/RFI interference and noise potential. Not sure if that's real or not but I worry.

From a pure numbers game, assuming you have a good connection and no competition Wifi has so much more bandwidth than audio will ever need, and I've heard good things about Wifi 7's ability to be stable even in a crowded environment, so, sure! Try it. 

Wired sounds better, especially in a transparent system

Wireless WiFi data connections for streaming work 100% fine as long as you have a strong connection.  That’s all I use.  The key term here is it’s just another network data connection.  You just need enough bandwidth to keep the data streaming.  There is no sound making involved until the data hits the streamer and then goes to the DAC.  Same story with modern hi res smart TVs.  All you need is the network bandwidth. 
 

I own a Cambridge Audio Evo 150 all in one  among other hifi gear. The only wires with that when streaming is to the speakers .  So nice and sound quality is top notch/ big league for sure. 
 

Obviously wireless subwoofers are a thing as well.  I use one with a tv soundbar but have not tried in a good system.  
Wireless technology for hifi is everywhere.  Young people use it with no remorse.  Old, set in their ways, 20th century vintage audiophiles:   Not as much.  
 

I’ve heard some very impressive sounding Bluetooth headphones recently. AptX lossless does CD resolution over Bluetooth these days. So there is now also that. 
 

I have no technical knowledge on wireless versus wired, just my own user experience.  My experience is that wireless can be much more convenient, when it is working.  At the gym, no wires is a must.  At home, a traditional CD player into a good DAC, seems to sound "better."  Maybe because there is no stress that it can't connect.  In contrast, almost daily Roon cannot find the core, taking 2-3 minutes of fiddling.  Connected, Roon is great.  In sum, whenever possible, I'm wired.

@bzawa 

Why not wireless connections between sources and amp and between amps and speakers?

The big fat wires normally connecting amps and speakers have to transmit power measured in tens or hundreds of Watts.  We are talking microwave ovens worth. by comparison, and you do not want to accidentally cook something in the radio beam, like a bird or your head.

Wireless data transmission over short distances usually needs only tiny amounts of power.  Many applications run for months or years on a single button-cell power source.

The only way to get rid of the amp to speaker wires is to put the amp(s) in the speaker box.

But you still need to run mains power so wireless is rarely actually wire less.