Why don't you provide examples, and comparisons on the amount of administrative savings compared to any extra burden created?
It's really quite simple. At one time if you were sending goods outside the U.K. you did not have to charge VAT on them. Now, if you're exporting to the EU you have to charge VAT at the applicable U.K. rate, and you have to keep separate figures for total sales to every separate EU country for the "Intrastat" reporting.
As you weren't even aware of how VAT is paid and reclaimed at each step along the sales chain though, I really have to question if you've ever been involved with a VAT-registered business or had to deal with VAT returns yourself. And in the foregoing debate about exempt and zero-rated items, are you actually aware of the practical differences between the two categories for businesses?