Being productive on the road was a big issue for me, so I'd stay places 2-3 months and then travel for 2-3 months. After 4 years and 50+ countries, i know where i want to spend most of my time, so in the places i really like, i just buy a small apartment. The truth is i could buy 5 apartments in south america for the same price as 1 back home.
As for mail, all my banks/credit cards use electronic statements now. Anything that requires physical mail goes to my brother or dads place, 99.9% of it is rubbish anyway.
Health services outside of western countries i find are just as good and reasonably priced, so if anything happens, ill just pay full price... which will probably work out less than a lifetime of paying insurance.