Bloodshed is generally bad for business. I would have thought that Vito's approach, imparted to Mike, would have been to look for a reason to kill, rather than a reason not to.

OK, so that's the obvious reason and the reason explicitly cited - the loss-a-respecta for giving in to Sollozzo. But Cuneo and Strachi were not directly mixed up in the Sollozzo/Barzini/Tattaglia thing.

Cuneo and Strachi, being small potatoes, would simply have sailed with the prevailing wind. IF the hit on Vito had worked, and Barzini and Tattaglia had wrestled the mantle from the Corleones, they would have followed. But S/B/T had failed - the Don lived - and Cuneo and Strachi, minnows that they are, would have continued to support the now victorious Corleones.

The deaths of Barzini and tattaglia would have been sufficiet to cancel out the respect issue. Cuneo and Strachi were plain unnecessary and, might I add, bad for business. Who knows how much disruption and loss of income was caused among their regimes (which the Corleones inherited)? Surely better to allow Cuneo and Strachi to continue, with a heavy tax payable to the Corleone family. Less blood, and more money.