I'm going to answer a slightly different question: were the titles merely coincidental? No. Army had a sustained run of greatness coinciding with the tenure of their great coach Earl Blaik.

I'm going to mostly use AP polls to prove this since they are the traditional yardstick used (keep in mind though that the poll only dates to 1934). Army finished 2nd in the AP poll in 1946 but claim the title through other polls. One don't have to concede it's wrong to count non AP championships as true championships but it's the common "objective" measurement.

here's a collection of all of the AP polls that army was in.

essentially Army was a nationally ranked team from early late 1930s/early1940s to 1960ish (Blaik went from 41 to 58).

For instance in Coach Blaik's final year 1958 Army was in the top 10 the entire year and never dropped below the top 5 after reaching that status in week 3.

After a 5-2-2 1947 season, Army had another great 3 year stretch from 1948 to 1950 as the lowest Army ever reached was 7th in the Nation and in 16 of the 19 seasons From 1941 to 1959 (first post Balik season) Army placed among the top 11 teams at least one time every year.

Balik came to Army from Dartmouth where he coached from 1934-1940 to great success including a 22 game unbeaten streak (including ties) and top 10 AP rankings. Essentially he was a hall of fame worthy coach (which is why he is in the hall of fame).

But while Balik was a legitimate hall of famer Army was a very good team in the 1930s bosting a 98-26-5 record which translates either to a .790 or .779 Winning percentage depending on how you count ties. On the other hand they played a substantially easier schedule (CFB average) than they would during their championship era (an elite schedule).

So while there is a role played by the growth of the Army pure football considerations have a lot of explanatory power on their own as a decent program is combined with a hall of fame coach

Thinking about this, I had a few related questions that build off of this:

• The question presumes that Army got better during this period due to changes in the Corps of Cadets, but what about the effect in the other direction? Did other college programs get worse due to a smaller pool of available students, especially of the most physically fit variety, which would be a problem not faced by Army in that period? I know that the NFL had to adapt during the period, so was it the case for the college game?

• Additionally, whether or not it is Army improving, or the competition regressing, this hypothesis that the war had an influence on Army's string of success would presumably also affect the Naval Academy, so is there any sort of appreciable, positive change in the quality of Midshipmen Football during that period as well?

Yes if only because it narrowed the field and disrupted the normal operations of other schools even more than at the academies.

For instance in 1942 Tennessee and Alabama(who had also calimed a national title in 1941 off one poll and a cotton bowl win) both finish with top 10 teams in the AP Poll. Then don't field teams in 1943 with most of the SEC except GT. In 1944 UT is able to finish in the teens by Bama finishes unranked. 1945 Bama finishes second and UT in the teens again. Since Bama was coached this whole time by Frank Thomas who had won a claimed title int he mid 30's as well, it is plausible that he could have fielded more consistent teams had he not lost a season in there.