Some speculate flutes were originally added to provide for grasping the cylinder of black powder revolvers while wearing leather calvary gloves to assist in turning it when bound up with percussion cap fragments and black powder fouling in the heat of battle.
Sounds as reasonable as "stronger" or "lighter".
All early Colt C&B revolvers had unfluted cylinders for strength with the iron cylinders used then.
However, there were a very few Colt 1860 Army Revolvers made in the "lightened" Texas model with cylinder flutes. The goal was to make use of spring steel of controlled carbon content and greater strength, but the fluted cylinder proved inadequate in strength, and sometimes exploded.(ibid Wilson) By the time the Colt 1862 Police came out, better steel and fluted cylinders were standard.
By 1873, the famous Colt Single-Action Army cartridge revolver came out, and of course it had a fluted cylinder.
By then, it could have been more for weight reduction then a hand grip.
However, calvary troopers still wore heavy leather gauntlets & shot black powder, so a better gripping surface & indexing flutes while reloading still might have made more sense..
At any rate, fluted cylinders have been used since cap & ball & SAA revolver days, and have become traditional now.
rc