After the killing of Sollozzo, Vito stays in the hospital for some more months while the Mafia war is going on, just like everybody expected. Now the combined power of four families against the Corleones was definitely more dangerous than Sollozzo, the Tattaglias plus a police captain. With Sollozzo alive Barzini wouldn't get his hands dirty. Cuneo and Stracchi are out of the game.
So by provoking a Mafia war, Vito's sons put his life in a greater danger than it was with Sollozzo. Why?