We've been here before. The Initial Teaching Alphabet failed because children still had to make the transition to conventional orthography. They would have to do the same with Cut Spelling.
Esperanto was an attempt to create an easy-to-learn lingua franca. Again, this is now a linguistic curiosity.
The argument about Italian children learning to read and write in a shorter time than their British counterparts doesn't hold water. Italian may be simpler than English. Japanese is acknowledged as the world's most difficult language, with students still being taught to read and write well into their teens. This hasn't stopped Japan becoming an economic superpower.
If spelling was simplified we would lose contact with our history embodied in the language.