Fixing it by harmonizing VAT rates would require treaty changes and be politically hard to hand one of the big financial levers to the european central bank, especially given not all countries are in the eurozone - imagine the US forcing all state sales taxes to the same rate, set by the fed, and you get the idea.
The U.S. is even worse off. There are nearly 10,000 sales tax jurisdictions in the U.S.
The solution is to reverse who is responsible for updating the tax rates. There are a lot more retailers than there are tax jurisdictions. It's stupid to force every retailer do duplicate each others' efforts and update tax rate data from every tax jurisdiction every day. Instead, make it the responsibility of each tax jurisdiction to update their tax rate on a central database every day. Every retailer can then simply download an updated tax table from the central database at the beginning of every business day. That completely eliminates the duplicated effort and produces the most efficient economic system (for distributing sales tax rates at least).