Radio

[YZ250]

I am puzzled that a radio is not available that can transmit its signal (Bluetooth?) to a speaker without the necessity for wifi/internet radio.

I'm sure it can be done very easily, it's just that I listen to radio channels online. 
This is my take on it (but I could be talking shite) 

Bluetooth is aimed at short distance, single Bluetooth usage, so you can play radio/music from a smart phone to a single Bluetooth speaker to amplify the sound from the phone.  If you buy a Bluetooth/Wi-fi Radio, you will most likely be prompted to set it up on a smart phone (via wi-fi or Bluetooth), as it is aimed at streaming music, hence you would have used up your single Bluetooth connection. My Radio/CD has its own Bluetooth/Wi-fi built in and searches for other Bluetooth devices, even when my smart phone isn't present, so I assume I could pair an additional Bluetooth speaker in another room to it. **I'll try it out later if I get time**. This is basically what you want.
We have an Amazon Echo Bluetooth'd to an additional Bluetooth speaker elsewhere and this works fine, but you did specify a CD player as well so this set-up wouldn't suit you.

With wi-fi, you can add multiple speakers provided that they are all capable of seeing your home wi-fi router network.

Shame we don't live closer to each other, as you'd be welcome to borrow my Bluetooth Radio/CD player and speaker to try out at your place.   

**Edit:
Just tried it and the Bluetooth radio/CD search found the Amazon Echo, which is a Bluetooth speaker, albeit with Alexa built in, so this set-up would suit your requirements. 

[Shackeng]

Thanks a lot, will get round to it when I finish my other projects.