The problem as reported is that many current payment methods used online either do not have such information, or the payment system being used (eg credit card via paypal) hides that data from the vendor, making it very hard to both provide a seamless checkout and capture the information required to levy the correct taxes.
That said, I'm really not sure that all this "two pieces of data must be collected" is as onerous as everybody is saying - the guidance seems much looser than that. For each transaction they want 2 consistent pieces of evidence of location, but the sources of said data are fairly broad & include ip address, some form of geolocation and the self reported location by the end-user, credit card location etc etc. Anything that the vendor believes to be reasonably reliable according to their data-model really. See guidance document here: http://ec.europa.eu/taxation_customs/resources/documents/tax... which amongst other things states that a country located account number (bank / credit card) combined with a customer self-reported country location is enough in many cases. (This is what Steam requests already btw.)
The problem for vendors is that the rules pushes liability onto them when they want certainty, plus the data storage requirements are fairly stringent (10 years!). The tax authorities are effectively saying: you can either collect enough information to be absolutely certain of the end-user location or collect less and carry the risk that an audit will result in big fines if we decide that you've been attempting to evade VAT by misrepresenting the location of your customers. This is of course no different from any other tax, but with a new system there's always some uncertainty to begin with until things settle down & no one likes uncertainty.