VAT in the EU is charged at the location of the purchaser not the HQ of the vendor. Multinationals pay 0% VAT in Ireland because although they're headquartered there the value add bit is realised elsewhere - i.e. where the sale is made. VAT is about the only thing the multinationals don't easily avoid by moving activity or profits to other jurisdictions.
The usual argument against using VAT is that it's regressive, as it hits everyone at the same rate regardless of their income. That ignores the fact that poorer people spend a higher proportion of their income on zero-rated items like food and basic essentials and less on luxuries, but it is at least a valid argument.
Amending the existing VAT rates is also a relatively simple change to existing tax law, as opposed to applying the clear and legally unambiguous "have they been taking the piss" test, as you've proposed. One of these is a practical solution to a problem, the other is an idea taken from a pub conversation about 3 pints down.
I post anon because none of your business.