You are the one making a surprising claim. It would be nice of you to support it.
Still, let me rephrase: how is that number arrived at? Who are the 50k?
It's not surprising at all.
As a general rule, there will be one crewed ambo on duty for every 50,000 people living in the service area, on the average, at any given time. That is (depending on the agency) 2 or 3 personnel plus the bus on duty per 50,000 service population. So a city of one million could be expected to have twenty crewed ambos on call at any given time, normally. Assuming that everyone shows up for work and all the busses are in working order. Which would mean around 160-240 total EMTs, depending on the rotation, and crew size.
Clarifying further: it is clear that cities smaller than 50k have operational EMS services with multiple crews and vehicles, so it is not 50k per crew. Implying this is so would be deceptive. That would be a greater number of personnel than the entire combined police forces of the Dallas/Fort Worth Metroplex.
It is crews
on duty, not total personnel. EMTs at home asleep do not render aid. How the crews are deployed are varied: some work 24 hours shifts like smokeaters, some 12s, some 10s, some 8s.
Leaving serial killers a convenient cover? Color me skeptical.
Serial killers are quite rare, and tend to have a signature. However, yes, that's why they tend to rack up a substantial body count before capture (if captured). Every local LE agency in the USA is autonomous. There is very limited sharing of data on a routine basis. Only in Hollywood do detectives get DNA results in less than several months, or full data including pictures off a fingerprint. Most departments do not have a dedicated forensics team, but rely on individual training and calling on State resources for major cases.
Most, if not all, states have an agency (in Texas, it is the Texas Rangers) which exists to provide trained investigators to assist (if requested) with high priority cases, such as murder, because most agencies will not have the experience base to properly investigate them.
For example, my agency experiences 3-5 murders a year, most of which are simple unplanned acts of assault which inadvertently resulted in death (a drunken dispute amongst migrants settled by brush hooks, for a common example). This would mean that our investigators would, on the average, act as a lead on a murder once every two years. The average tenure of an investigator was six years, which means just about the time they started to have sufficient experience to really manage a murder case, they were transferred or left law enforcement. Since investigations (as in many agencies) is a career dead-end, this means that the supervisors over investigations normally are not former investigators, but rather career patrol officers who have advanced in rank.
Hence the need for the Rangers.
And why today's serial killers tend to be mobile, and work the less populated jurisdictions. Gone are the days when the Green River Killer or the Atlanta child killer could work one area with impunity; these days, once identified, a task force will be formed with experienced outside help. But if the murders are scattered over numerous jurisdictions spread out over a sizeable area, a pattern may not be noticed for years.