As mentioned Michael wanted more money, legitimacy and power.
Ultimately both Michael and his father wanted legitimacy for their family (criminal and personal). So it was a sort of progression.
Vito has to muck around in numbers, bookmaking, extortion and other slimy activities. He's outside of the upperworld. But the money and power he builds up doing this is transferred to Michael who uses it to "purchase" legal casinos and hotels.
Michael straddles the upperworld and underworld but builds even more wealth than his father did. Then the next generation that comes after Michael is completely removed from any sort of criminal activity but has enough resources to own international banks, huge shipping interests, sports franchises, and so on.
"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming
Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.
| 
