Square needs to comply with all Australian financial and privacy legislative requirements when operating in Australia. They are also required to report suspicious activity to the relevant agencies, no different to banks and other financial providers (e,g. credit card providers).
Square does collect information, especially from the Square account holders (the merchant) but it appears that little is collected of the customer…unless say detailed customer details are manually entered in Square. A tap and go (paywave) transaction without an issued invoice is unlikely to generate any more collected info than any other retailer.
There are many retailers which offer digital receipts to a printed one (Bunnings is possibly a well known example). Digital receipts have the same legal status as printed ones, but possibly less likely to be lost or fade over time. I suspect that inthe future, more and more retailers will move towards digital receipts to reduce costs and also save paper waste.
It is also worth noting that Square merchant fees are higher (about 1%) than that afforded by the banks, and if one processes more than about $3000-3500+ per month using Square, the bank issued EFTPOS machines become more cost effective. Square market is possibly more towards very small business with low turnovers, rather than larger small, medium to large businesses.
BTW, we are exploring using Square for a small business we will be running later next year and have been weighing up the pros and cons from a merchant viewpoint. There are also other providers which compete with Square and traditional bank EFTPOS entering the Australian market place. On a positive note, these other providers provide competition to the traditional bank run system.
Maybe a comparison of emerging technologies with traditional ones could be a test for Choice…to evaluate these from a consumer perspective.