It is a comfort thing for me (at the airport). If I am flying I am probably balancing a toddler who demands to be held - and perhaps MUST be held while running down the terminal. And a DH who is terrified of flying and must metaphorically have his hand held at the same time.
Also, running shoes are often the bulkiest shoes I am taking, and I prefer to wear them and leave more room in my bag
The only issue I have with it, is I don't have that convenient back pocket to stash stuff in (ID, boarding pass, tissue). I generally wear a tank top and hoodie with pockets to solve that.