Why did no private company or government try to bring radio communications to general public like we have cell phone today? What were the hurdles and challenges?
The radio spectrum is limited. There are is only a finite range of frequencies over which we can transmit so you if have two people communicate by directly transmitting to each other over two frequencies, no one within the maximum transmission range of either user can use that frequency. If the maximum range of those users is very large, then that means very few users.
If you you only have 100 frequencies you can use, and your range is everywhere in the city, that means you can only have 100 users per city.
It's like if everyone spoke with a voice so loud you could hear them for kilometers in every direction. No one would be able to hear each other unless very few people were talking per area. But if everyone's voice doesn't reach very far, a lot more people can talk to each other in the same area.
That's why we use cells. Do you know why a cellular phone is called a cellular phone? Instead of directly transmitting the radio signals to each other, cellular phones use weak radio transmitters that don't go very far. We then place cellular towers everywhere so that there is always a nearby tower to pick up the weak signals from the phone, and the signal the tower sends to the phone can also be weak.
Since the towers are connected together by cables, they don't use radio bandwidth and since all the radio signals involved are weak, they do not travel very far so nearby areas can re-use that radio frequency. So we can have many users per area. The area around each radio tower in a cellular phone system makes a cell within which frequencies cannot be re-used. But the same frequency can be re-used in two adjacent cells.
Your premise is wrong. Governments and private industry did indeed expend great efforts to bring radio to the public beginning over 100 years ago. This was quite successful and until the invention of television, most homes had radios in them for receiving news and music.
Those radio facilities covered both local broadcasting (within 50 to 100 miles) and long-distance broadcasting (up to 5000 miles).