Been There, Done That.
Your idea has been done, countless times. But,the advantages of the real internet outweigh the disadvantages. China has tried to just operate it's own internal internet. Many Corporations do also.
But the real internet was beckoning, and the countries found that it hurt them more to not use the internet. So, they use the internet, then try to control the people. The list of those who had done that would include China, Viet Nam, Cuba, Venuzulea, Iran, Egypt, Syria, Myanmar (Burma) and the list goes on. That includes the UK, the US, Germany, Italy, Australia and Russia too, by the way.
In the end a means of communications that doesn't let you communicate just isn't very useful.