Why is stick/shove/etc up one's ass much more common than in/into one's ass?
The former is a more aggressive description of the act being used as a metaphor. Well, mostly as a metaphor. One would never say the nurse "stuck a 250mg acetaminophen suppository up . . . ," rather one would say that the nurse "inserted a suppository into my. . . ." The more aggressive makes a stronger metaphor.
One part of the answer may be that ass, or arse, has got two different meanings.
Ass, or arse, has the same meaning as buttocks or bottom, as in: "The nurse said, 'Right then. Don't just sit on your arse!' No sooner had I got up than, without so much as a Howdydoody, she'd stuck the needle in my arse."
The prepositions on/in are used because here ass or arse refers a solid object.
However, arse is sometimes used to replace the more technically correct arsehole (a three-dimensional space).
"Then, to make matters worse, she'd stuck a suppository right up my *arse/arsehole! When I told her that she had promised it wouldn't hurt, she just replied, "Well, I guess I was just talking out of my *arse/arsehole."
I don't know what it would be like to have a suppository shoved in my arse (solid object), but I'd rather not find out.