It was been roughly 100 years since the world's larger militaries began to adopt semiautomatic pistols. American police began their wholesale shift to pistols over 20 years ago. It would seem that revolvers are a dying technology. Why would anyone choose a double-action revolver?
There are several reasons. The chief operating characteristic of a revolver is that none of the energy from the discharge of the cartridge is used to operate the revolver.
[1] The revolver's mechanism is operated by the squeezing of the trigger, which rotates the cylinder, cocks the hammer and then releases the hammer to strike the primer of the cartridge. This is what gives the revolver its advantages.
First, the mass of the revolver is independent of its operation. If you want a .357 that weighs less than a pound or is close to three pounds, you can buy one. With a pistol, there is a size limit for any particular cartridge below which the weapon cannot go, as the slide cannot open the chamber until the pressure drops to below certain levels (which is why some pistols are "blowback" operated and others use a variant of John Browning's locked breech system).
Second, because the operation is so simple, there is less to go wrong. There are no "tap-rack-bang" drills for a revolver. The manual of arms for a double action revolver, especially the S&W shrouded-hammer models is as simple as "load the cylinder, close the cylinder, aim, squeeze the trigger to fire, repeat until empty, open the cylinder, eject the spent cartridges. Repeat as needed." The rest is just practice.
Third, because of the method of operation of a revolver, there is no issue of "limp-wristing" to cause a malfunction. Some pistols will jam if the shooter does not hold it firmly. True, revolvers can jam, but it is a rare occurrence compared to a pistol.
Fourth, because the energy of the cartridge is not also used to operate the mechanism, you can fire any round that will safely shoot from the weapon. In a .357, you can use everything from primer-operated wax rounds for training to heavy 158 grain soft points. You can shoot wadcutters or .38 Specials on the range for practice, which is a real plus when your revolver is one of the featherweights, as long as you occasionally shoot your full-power carry load so you know what to expect. Yes, the point of impact will be different, but I submit that at the typical ranges for close encounters of the deadly kind, the difference in the points of impact between target and full-charge loads will be insignificant at best.
Fifth, revolvers are dirt-simple to operate, which means in a bad situation, when your heart is racing and adrenalin is flowing, there is nothing to remember, no intricate steps to perform. Aim and fire. It also means that there is less training to be done. If you cannot spend a lot of time at a range, a revolver is a better choice.
(Soon to come-
the other side of the argument)
[1] Yes, I know about the Webley-Fosbury Automatic Revolver.