I would also prefer to fill out the app at home so I could double check phone numbers, use my best handwriting, attach a fresh copy of my resume, etc.
I have only applied at two places that required filling out the application in-house, the first was an assembly-line production type place so I think my question of "why" has been aswered by those that suggested they were checking for literacy.
I had been to lunch with my friend who worked there and she mentioned that they were hiring for office help so I asked the receptionist for an application. I was completely put off by it because I was not prepared to sit down and list phone numbers, etc. off the top of my head (so unfortunately I'm sure some of them were wrong, in retrospect I should have come back later to fill it out, I'll blame youth
). I carried past job/reference contact info with my from then on so that I was prepared for the second time.