Why doesn't The UK Create A Common Wealth Union To Compete With The EU?

Because the Commonwealth counties are too scattered and to disparate to make such a union.The point of the EU is that it is a group om very similar countries with similar climates, similar wealth, similar levels of education etc. .....
and therefore it was bot easy and efficient to reduce the barriers between them. My feeling is that one of the problems with the EU was that some of the Eastern countries admitted in the 90s and early 2000s are too dissimilar from the original core, and the assumptions on which the U was based, of common interests, have nor held true.

The Commonwealth has far more dissimilarity, both of wealth and culture, and of geography, to be anything more than a pleasant talking shop.