"Quicker and easier" is not always about syllables. Mikey is easier to say than Mike even though it has more syllables.
But the acronyms used by emergency services, police, medical, and military are all jargon within those fields. They are actually communicating more information to their co-workers than just a general physical description. A "gunshot wound" is a layman's term that might be used in a general way in conversation, while a "GSW" describes certain protocols and procedures. A specialist might need to be contacted, or there may be specific paperwork involved to complete the job. For instance, all gunshot wounds have to be reported to the police, but it probably requires a ranking specialist to officially declare a GSW, but with protocols in place for reporting a potential GSW to the proper channels.
Crime and medical dramas are attempting to sound more authentic by putting jargon in the mouths of the characters. Ask an ER nurse how realistic a medical TV show's dialog sounds and you might get a belly laugh. Ask any scientist about the technobabble in Star Trek, which is an affectation of the same idea.
An NYPD sergeant once told me the most "realistic" cop show he'd ever seen was Car 54, Where Are You? (a farcical comedy from the 1950s), mostly because they had all the ranks and protocols correct. The show is set in a made-up precinct and the plots are ridiculous, but the jargon they used is still mostly correct 50 years later. He said all the modern crime dramas are just layers of soap opera/Hollywood; no one ever really discusses dramatic or poignant personal issues at work. His biggest peeve is that recurring actors who are paid to speak lines give information far outside the scope of their job for the convenience of exposition. No amount of authoritative jargon is convincing when it is spoken by the wrong person.