That's one thing I'd disagree with. My perception, nothing more, is that your statement would have been true of the the smaller police forces. In places like NYC, getting on the police force, and maybe fire department, was for some a way to beat the draft. Don't know what the ratio of military to non-military has been on the PDs but it would be interesting to find out.
History is largely about human perception and I speak as a teacher of American History and sociology. But remember the era of which we speak. Was the police department an honored organization in the opinion of the nation's youth (draft age)? Uh-Uh. They were called FUZZ or PIG and more and more were in direct and bloody conflict with the youth whenever the moratoriums and sit-ins left campus and took to the city streets against the war in Vietnam. Even on campus there were many conflicts (remember Kent State? That started with the cops and escalated to the guard).
As late as the 1970's when I first took on the notion of being in law enforcement (a dream I wouldn't realize until 1986 after I got off active duty) and discovered that a requirement for the Miami Police was prior service or a college degree in lieu of military service. This was before massive minority and female recruitment changed those standards in the early 1980's.