From a story I wrote for NZBusiness on the evolution of device screen sizes:
…Kantar Worldpanel, another research company, points out, there’s a practical limit to mobile phone size. Kantar says phone buyers gravitate to devices in the 4.7 to five inch range. It doesn’t matter how thin and light devices are, anything bigger than five inches can’t realistically fit in a pocket.
Kantar reports that in 2013 the majority of people with phones smaller than 4.4 inches switched to a bigger device when they replaced their phone. Most of those who started with larger phones didn’t move up a size.
So there you have it, people have decided the ideal phone screen size is more than 4.4 inches, less than five inches.
If a phone screen isn’t big enough for you, folding phones are a useful alternative approach.