I did read a well researched book (The Big Roads by Earl Swift) on the US highway and interstate system's creations, and I don't recall that being mentioned as a primary motivation. The main motivation for beltways and such really was just "alleviating congestion"
I didn't bother looking this up yet again to reconfirm I'm not misremembering, but I think the onus is on you here since it's a weird claim even if oft repeated.
Edit: I immediately looked it up anyway. Military thinking did factor in in early planning/rabblerousing regarding highway construction, but this was very abstract and DECADES prior to the main effort of highway construction. There is not really a strong historical connection, and the military did not play a leading role or even much of a supporting one, at the time the interstates were actually built much later.
At the time most interstates were built, the main justification for Congress to spend the money was civilian use for alleviating congestion, which is why (Eisenhower famously was baffled by this) the focus was on intracity expressways, not intercity ones.
See https://en.wikipedia.org/wiki/Interstate_Highway_System#Plan...
I would guess the biggest reason for this myth is they were built under the executive sponsorship of Eisenhower, who at some point mentioned the anecdote that as a young man he had coincidentally been involved as a junior officer in an experimental military convoy from coast to coast in the 1910s. Ironically, Eisenhower's connection to both was peripheral. In one he was just one of many cogs in the machine, in the other, decades later in life, he was just the guy who did the politically expedient thing and signed on the dotted line for plans that had been developed and advocated by others. But there was no causal relationship between these two events.
Of course, people love a good story, so this quickly mutated into "General-turned-President Eisenhower remembered how bad the roads were for the military and masterminded the interstate system to fix that problem" which is a complete mischaracterization. He was a very, vey popular figure in his day so modest mistakes like that that made him look better were not likely to be corrected. For one of the main generals who "won world war two" it would have been a believable claim, as well as something one would _want_ to believe.
The reality is the big roads came about for the boring reason that cars were becoming more popular.