At the cost of complexity and acting as a honey pot for criminals. I have to deal with VAT for a business I help to run and it's very complex. The bigger problem in the EU are the large amounts of carousel/VAT fraud.
Most of the complexity comes from a backward compatibility and the fact that politicians creates exceptions for certain products to gain votes. If the tax was the same for everything it would be much simpler.
Fraud is a solved problem, especially if you can start from a blank slate like in US.
Governments are trying to reduce the fraud, but they are super slow.
https://en.wikipedia.org/wiki/SAF-T