Right, Enzo: he was the most powerful and influential gangster of his era. He had tremendous political clout, and could settle a strike with a single word. He ran a network of high-society gambling and opium dens, and imported high-end booze. But he also had a big network of up-and-coming gangsters whom he staked to money and territory, and who looked up to him as a mentor. Frank Costello, Charlie Luciano, Meyer Lansky and Bugsy Siegel were among his proteges. Luciano, in his autobiography, said he wished that Rothstein had lived longer--"he woulda made me into a gentleman, like him."
Keep in mind that, during Prohibition, the Mafia was relatively small time and local. Most Mafia families were content to look after the rackets in their own neighborhoods, running them as they had the Sicilian villages where they came from. Jewish and Irish gangsters ran the booze and other major rackets in almost every big city. Italians were the biggest players only in Chicago--and Capone's "Outfit," as has been stated here many times, was not a Mafia family.
Everything changed with the Castellemmarese War of 1930-31. After Charlie Luciano (with Lansky's help) got rid of the "Moustache Petes" and formed the Commission, the Mafia began to be a major power in interstate and international rackets.