Actually, suppressed handguns were in limited use by US forces in Vietnam.
.38 revolvers were relatively popular for use when clearing tunnels and bunker complexes. Most common were S&W Model 10 and Model 12 revolvers (standard issue in Army aviation units at the time), and some were equipped with suppressors that locked onto the barrel by a half-turn engaging the front sight in a recessed cut. Not terribly effective, but the reduction in noise and muzzle blast was noticeable, especially inside an enclosed space. My understanding is that these suppressors were made in US Army maintenance machine shops in Vietnam. S&W manufactured a specialized version of the Model 29 .44 magnum as a "tunnel gun" with very short barrel and cylinder modified to accept a special round loaded with multiple projectiles (these have been discussed on the forum before, and although not suppressed they are an example of specialized equipment for certain situations)...