Except in cases where people are evil for evil's sake (which is not the case for The Godfather), most criminals consider crime to be a necessary evil to achieve what they want.
- Robbers rob people because they want money, not because they enjoy robbing. Even though it may be their preferred money making method, it stands to reason that most reasonable people would avoid committing robbery if they had access to the benefits (money) without needing to rob people in the first place.
- Murderers generally murder people because they want to eliminate that person (or they have been hired by someone who wants that person eliminated). Except for pathlogical serial killers, it's never a matter of murder for murder's sake.
- A loan shark only uses violence to punish those who no longer pay back the loan. Their main activity (loans) usually doesn't attract police attention (because their clientele wants a clandestine loan), but without violent retribution for non-payments; they can't actually ensure the success of their loans.
- Mob families often commit violent crimes in order to ensure the success of their non-violent activities (which may still be a crime in and of itself, but there's less force behind such an investigation).
But the Corleone family is a succesful business. Their success is built on their criminal history, but their current state renders them able to continue their enterprise without needing to commit any further crimes.
Not committing any further crimes strengthens the enterprise, by no longer being vulnerable to police investigations.
Furthermore, if they encounter any dispute with another family who does still commit crimes, they can have the police and the courts by their side.
When two criminals have a dispute (e.g. I bought drugs from you but they were fake!), they settle it without getting the police involved. However, if one party is completely legit, they can involve the police if they so choose without it blowing back on them (e.g. I bought a car from you but it doesn't work!)
Longstanding criminal enterprises (whose main goal is not crime for crime's sake) that have proven to be sustainable will generally try to go legit once their enterprise is capable of doing so.
Sons of Anarchy, Narcos (the Cali cartel in S3), The Godfather, ... They all try to go legit.
There's also plenty of real world examples, e.g. Jordan Belfort (the real Wolf of Wall Street) has cleaned up his act because his current skills (that he learned while doing shady things) are able to turn a profit legally. Many hackers/crackers do the same, they can end up in security positions trying to defend their employer against digital attacks.
If you can avoid the problems (incarceration), without losing the benefits (financial stability, power), why wouldn't you?