Barzini probably could have financed Sol by himself. But, as Lilo and Apple noted, Vito "controlled all the judges in New York." So, without his protection, the drugs business would always be endangered.

I've often wondered why, if Sol needed Vito's judges, he tried to kill him, thereby losing, as Tom predicted to Sonny, "half our police and political protection." Wouldn't that mean that Sol would lose access to them, too? I believe that Sol's (and Barzini's) strategy was that Vito's death would gravely weaken the Corleones. Then Sol could dicker for the remaining half of the Corleones' politicos and judges at a bargain rate. The other half wold be fair game for Barzini to purchase. I also believe Sol's attempted murder was not only a "self-respect" thing, but a ploy to make himself a pezzanovante with the other Dons. And, while they wouldn't try to kill Vito on their own, if Sol was willing to do the job, why not let him? Barzini, in particular, stood to gain: the Corleones would come after Tattaglia (as they did with Bruno), and he'd pick up the pieces (as he almost did).