This fantastic New Yorker shirt cartoon (June 8-15 combined issue, page 67) about non-iron shirts reminded us of why we'd prefer to iron!
While non-iron is certainly convenient our shirts are not treated with wrinkle free processes because we really don't like what it does to the fabric or to people. Wrinkle-free treatment actually involves dipping shirts in a formaldehyde resin bath which has a number of problems:
(1) formaldehyde is a known carcinogen, but for a variety of reasons continues to be unregulated in the US and, amazingly, companies aren't even required to disclose the use of formaldehyde in products. In fact, treated shirts will continue to release it over time (this is a good article on the topic if you are curious -- http://www.nytimes.com/2010/12/11/your-money/11wrinkle.html…)
(2) non-iron treatments tend to reduce the shirt's longevity as the fibers break down more quickly
(3) non-iron shirts tend to be a bit scratchier and less soft on the skin
(4) non-iron treatments make shirts less breathable
Fortunately there is a good alternative to this: use very high quality fabrics that are made from quality long-staple cotton (which we do). They're more naturally wrinkle resistant that way and without all of the downside from treatment processes.