Why did they pick Slyvester stallone?

I don't think that matters it's how you portray this character have you noticed not much of what you see on screen is the same

Alcohol and leprosy are Very similar, too much of either and you'll end up legless

And why not pick Stallone? I believe his portrayal of Carter is very authentic. I can imagine Stallone as Carter the mob enforcer. He gets the job done, is very tough and shows some compassion when needed. He's not unbeatable but knows how to overcome and gets results. I also liked Alan Cumming's role as ITC tycoon Jeremy Kinnear. Cumming does a convincing job playing a young elitist computer mogul who lives his life in a bubble until he encounters Carter. Carter 'bribes' his way into a private golf club and gets a one-on-one meeting with Kinnear (Cumming). Kinnear realizes it's in his best interest (Carter sort of threatens him) to share what he knows regarding his business interest with low level mob guy Cyrus Paice (Rourke). We learn that Paice has invested into the adult industry that includes prostitution. And Kinnear gave Paice some front money. Paice has an adult club and caters to an adult orieted clientele. He nows considers himself a 'respectable' businessman and cares little about Carter's interest in his brother's death. And then we have Carter who cares less about Paice's business affairs but wants to know what Paice has to do with mysterious death of Carter's brother. Oh what a tangled web we weave.
Anyway Stallone is very convincing and I'm sure Michael Caine played an equally convincing Carter in the early 70s.

"Why did they pick Slyvester stallone?"
Jude Law was unavailable.

They went with Stallone because other real actors read the script and threw it in the trash. Stallone, on the other hand, specializes in making crappy movies, so he was more than happy to sign on,

Why should that surprise you?

The 1971 movie is a British production. The 'mob' in Britain are English lower class and Irish.

In America the mob are Americans of Sicilian or Italian ancestry. It wouldn't make sense to make them anything else.

From reading the trivia, it seems that the producers wanted to do a crappy movie as an action vehicle for Stallone, rather than the great movie the director and Stallone signed for. The producers want money, and there isn't much that an actor or a director can do.