Vito still held the trump card over the other families -- he had the politicians and judges in his pocket (this was brought up even as late as the peace summit after Sonny's murder). The Sollozzo hit on Vito was aimed at loosening that grip on those groups -- even as Vito was in surgery, the rest of the family was calculating how much of a blow it was going to be to the family.

The Corleones had far too much downside risk with the original Sollozzo deal. As Turnbull pointed out, it would have helped Barzini out, mostly by instantly giving him access to the protection from the law that Vito had spent years cultivating. Barzini can use his resources elsewhere, such as moving on Vito.

To use a historical analogy, it's like the atomic bomb development. The Soviets were years behind the Americans in development, until the critical intelligence and knowledge was virtually handed to them. Instead of being years behind the Americans, seemingly overnight, the Soviets were on par with the Americans.

By saying no, Vito could avoid the stigma of the drug trade and better keep those judges and politicians in line. When narcotics inevitably ruined neighborhoods, the attention from law enforcement would be directed to the other families involved and away from the Corleones. From a perception standpoint, the Corleones would remain more legitimate than the families in the drug trade, and thus more sympathetic from the general public.

While Sonny was hot for the deal, I doubt that Tessio and Clemenza would have usurped Vito. There was far too much respect for them to turn against him. The discord in the two capos was much more apparent after Vito gave his consent to narcotics and the other families started chiseling on Tessio and Clemenza's turf.