...When I was recently (December 2016/January 2017) in Australia and New Zealand, I purchased country-specific SIM cards for my unlocked iPhone 7+. Worked like a charm.

I was gone for 6 weeks total. My US carrier, AT&T, wanted US$120/mo for international roaming. Instead, I swapped out my SIM card on arrival in Sydney (enter new Australian phone number.) Cost me $AU40 cash, and that lasted me from Dec 9 (arrival) - Jan 1. Upon arriving in New Zealand on Jan 1, I think I spent NZ$20 or so for 2 weeks of NZ cell service (complete with a brand new NZ phone number.) On Jan 12, when I got back to Australia, my original plan from Dec 9 had expired, so I had to spend another AU$10 for my remaining 5 days in Sydney to reactivate my Aussie SIM card.

All SIM card activations were done in the respective airports (Sydney/Auckland.) In Sydney, I used Aussie cash. In New Zealand, I used Apple Pay. (Interesting side note: I spent 12 full days in New Zealand, and not once did I ever have New Zealand cash in my wallet. EVERYTHING was either Apple Pay or credit card.)

I still have my Aussie and NZ SIM cards, just in case I ever decide to return.