As someone whose mouth was so small that I had to have four permanent teeth other than my wisdom teeth removed before they could put braces on my teeth to straighten them, I find this a major problem–not to mention that seasonings like mayonnaise make the whole sandwich slide apart in a mess anyway.
When we go to our favorite Greek restaurant and get a gyro sandwich on pita bread, we tell them not to roll it, and then eat it with a knife and fork as an open-face sandwich.