In the last 2 years, I have travelled through 22 US States, the Caribbean, UK, France and Spain. In the last three weeks alone, I have clocked up 1000+ miles per week in 3 different countries. During 90% of that time, my phone has been on airplane mode after being hit with substantial bills for roaming charges a couple of years ago. Public WiFi is the answer.
Living without a mobile number is not as tough as it seems as long as there are plenty of places to access wifi.