Sounds too messy for Barzini's taste.

Seeing as how the judges & politicians were in Vito's pockets like so many nickels and dimes, they would probably be loyal to the Corleone Family. Barzini's attempting to muscle in might be sufficient enough reason for a war, without his ever having fired a shot.

Whether they anticipated Don Corleone's turning Solozzo down or not, there was a certain way they had to go about this. His refusal to cooperate gave the red light to have Vito eliminated thereby open the door to work with his son(s). Strictly business.

Even with these people there was a certain amount of 'decorum' involved.

Apple