The real reason that semi-autos didn't see common or widespread law enforcement use in the US until the '80s is because of ignorance and outdated knowledge among the people who set policy for major law enforcement agencies.
Oddly enough, some of those very same flawed opinions are still prevalent today. Such as: "There's also the fact that automatics weren't as reliable as revolvers with all the moving parts and springs and power of the ammo moving a slide."
Bollocks. By the late '70s semi automatic pistols had gone to two world wars, Korea, Vitenam and a host of minor conflicts the world over.
Take a look at the policy statements and training coming out of law enforcement agencies during the transition period and you will find it's rife with ignorance of semi-autos. There's a very good reason why the first generation of semi-autos used by police agencies in the '80s were almost always SA/DA with decockers and/or safeties. That would be institutional ignorance and fear based on inexperience with the technology. Remember, the guys writing the rules rarely have hands on experience with the equipment. So, when it came time to catch up with new technology, the guys writing the rules reverted to what they knew best, old technology. They mandated that the new semis be as revolver like as possible.. oh, and that they have safeties and deckockers. Never mind that the revolvers didn't have safeties. Shut your mouth you dirty semi-auto heathens. It took until the '90s and the retirement of most of those old hats before institutional thinking on semis began to change and guns like Glock started gaining market share over the old DA/SA guns.
Of course, you still have examples of institutional stupidity enforced by revolver thinking, like the NYPD and the "guaranteed to shoot bystanders" NY1 trigger.
So, the short answer to the question of why the transition to semis took so long with American Law Enforcement is... Fudds in uniform.