I just looked it up and apparently Dwight Gooden baseball nickname was Dr. K (which isn't very memorable as I've never heard it before), which got shortened into 'Doc'. Roy's nickname of 'Doc' is a play on his name, coined by Tom Cheek as a reference to Wild West gunslinger Doc Holliday.
I'd agree with you about The Big Unit and The Big Hurt (and The Crime Dog and The Iron Horse). Sometimes you 'hit' and the nickname really sticks. It just seems to me there are a lot more misses with those forced nicknames (The Process has to be the worst ever) like:
Vlad the Impaler
The Professor
The Hebrew Hammer
The Splendid Splinter
The Yankee Clipper (prefer Joltin Joe)
The Wizard of Oz
I'd rather see the likes of:
Big Mac
Miggy
Ryno
Yaz
IMO, nicknames are something people typically refer to you as. Nobody goes around and says "hey The Process do you want to grab a bite to eat tonight after the game?"
Nobody would ever call Pearson "The Airport" in the dressing room - because that would be stupid.