In the US, perhaps. Chip and PIN is the standard for new credit and debit cards in the UK - swipe and sign isn't quite obsolete, but it's certainly on the way out.
This can be a big inconvenience for travellers from the US to the UK (having worked in a theatre box office at the Edinburgh festival, I can testify to this). If Square takes off in a big way in the US - I imagine it will - it'll be similarly inconvenient to visitors from the UK, Europe and elsewhere.
Square is meant to be an entry-level credit-card terminal, meaning it's targeted toward businesses that previously did not accept credit or debit cards of any kind. It's misleading to say that Square causes an inconvenience for foreign travellers, since the businesses using it previously did not accept any kind of plastic payment whatsoever. It only adds convenience, though not as much convenience as foreign travellers may desire.
This can be a big inconvenience for travellers from the US to the UK (having worked in a theatre box office at the Edinburgh festival, I can testify to this). If Square takes off in a big way in the US - I imagine it will - it'll be similarly inconvenient to visitors from the UK, Europe and elsewhere.