Being head of a family demands respect. If you ain't got respect, you ain't got a family. So, while EA's The Godfather may look like a tempting excuse to 'bada-bing' people full of Tommygun lead, we're assured it'll take a lot more than that to become a successful Don.
The combat system is the prime example of using fear over fists. Although it'll be perfectly acceptable to feed a few knuckles to rival families, the use of Fight Night-style analogue stick punches lends a depth to the brawls that'll be needed to induce knocking knees and brown trousers. Instead of hitting someone, if your reputation is high enough, all you'll have to do to beat someone in combat is to raise your fists and watch your pathetic no-mark opponent cower in terror at your power and influence. Subtle intimidation and threats often beat the bone-headed fisticuffs of low-rent thugs.
You won't be able to intimidate or harm anyone willy-nilly, either. Although it's possible to mow down an old lady for fun, no amount of police bribery will prevent that kind of behaviour from bringing the full force of the law down on your head. Thankfully though, when 'disagreements' are kept within the family and can't be resolved by mere threats, you'll be able to resort to using your fists, or pulling your trusty pistol. And even guns can be used for tasks other than killing - waving them around in front of someone's face can get the job done just as easily, and if that doesn't work, a shot to the kneecap is often more persuasive (as well as good for extracting confessions).
It's easy, really. If you crack an illegal gambling ring on the family's turf, don't go in all guns blazing, just leave them a friendly reminder not to do it again. Like the head of a horse, for example.