Imagine the complexity of correctly accounting for a VAT when rates vary dependin on product type -- and doing it across an entire national economy! I'm glad they don't support that for as long as they don't have to.
Is it doable? Sure. Does it need resources that could be more fruitfully applied elsewhere? Probably.
Funnily enough only EU country with no reduced rates on some products is Denmark. So pretty much any system used in other countries already takes this in account.
Is it doable? Sure. Does it need resources that could be more fruitfully applied elsewhere? Probably.