Yup. And that war in particular did lead a number of countries in Europe to start building royal or standing armies.
You're totally right. That's why hold that Vietnam did more for our national attitude about the military as we watched on a daily basis film on TV from both Vietnam and the anti-war protests sweeping the US. Canadians revelled in the fact that it wasn't us there; and that we were fulfilling peacekeeping duties in places like Cyprus.
Americans developed a part of their country that greatly supported the military (and the draft) and another part that deeply despised the military. That later attitude was consciously reversed by a largely reformed volunteer army. Grenada, for example did not result in the national hatred of all things military as Vietnam did. By Gulf 1 it was a love fest. That was when the US public, in general, returned to having pride in its military as a fighting force and not merely a road to GI Bill benefits.
Canadian reaction to Vietnam was an ingrained sense of; "Not us." The country revelled in not becoming involved in conflict like the US and firmly believed the only need for a military was to do the peacekeeping. We gave up nukes and constantly shrank the real warfighting capabilities. Trudeau wasn't an aberration. He was a reflection of the national consciousness of the time. Even the October crisis didn't dispel that.
In short, when you look at where Canada's view of the military stands now, all you have to do is look back at the 1960s. That decade, reinforced by 50 years of peace, is what built the nation's belief system. Few of today's people remember those days, but the beliefs and attitudes formed then are now subconsciously deeply ingrained. The country has already forgotten Canada's military role in WW1 and WW2 (except for one day per year) so the colonial, frontier experiences of the 1700s and 1800s have only the tiniest effect.
IMHO, if we truly want to build a proper military, it starts with the kids - cadets - you bet, but you really want the high school kids. They're looking for a mob to be part of; they want to find pride in what they do; they want guaranteed full-time summer jobs; they want help to pay for their higher education. We do some of that but the military needs to double down on it several times over. You do not change several decades of attitudes by sitting back and hoping for the best. You need to be aggressive. Year-long waiting lists to get in or post enrollment waiting for a course are just plain nonsense. The military, especially the army, has a fetish for keeping initial individual training mostly away from the units and leaving it to under resourced schools. That might work for a fully resourced army but currently there is a need for a massive multi-year surge which heavily involves the units.
But I digress.