Here is a frame challenge.
The OP says that Juan Rico seems to have ended his formal education with high school, and yet has enough more education than his friend Ace that Rico can go to officer's school and Ace can't. The OP can hardly believe the possibility that Ace could have entered the military without completing high school.
Why would someone in the year 2022 believe that Heinlein writing in 1958-1959 would assume that a military of the distant future would require a high school diploma to enlist?
When did having a high school diploma become necessary to enlist in the US armed forces? It wasn't during the 19th century when there were many teenage and younger drummer boys in he army and first, second, and third class boys in the US navy. I think that if I mentioned the ages of the youngest 19th century recruits in the US armed forces, most people here would find it unbelievable, more like science fiction than history.
It wasn't a requirement in the US Navy in World War Two. Calvin Leon Graham (April 3, 1930-November 6, 1992) was an elementary school student when he enlisted on August 15, 1942, aged 12 years, 4 months, and 12 days.
Of course a boy who could pull off such a big lie about his age might have been able to pull off an equally big lie about his education.
This site says:
During the enlistment for the war, young boys had to be at least 17 to be allowed to join. At 16, one could join with a parent’s consent, but 17 was still preferred. However, Graham was undeterred. Along with two of his friends, he forged his mother’s signature on his enlistment papers, stole a notary stamp from a local hotel, told his mother he was going to visit relatives, and lined up.
If 17 and even 16 year olds could legally enlist with the permisssion of their parent's I doubt a high school diploma would be required, since only a small minority of boys that age would be high school graduates.
There is a book about underage US soldiers in World War Two:
And that should say whether a high school diploma was a requirement for enlisting them.
Dan Bullock (December 21, 1953 – June 7, 1969) was a United States Marine and the youngest U.S. serviceman killed in action during the Vietnam War,1 dying at the age of 15.
When he was 14 years old, he altered the date on his birth certificate to show that he was born December 21, 1949. He processed through the recruiting station, and enlisted in the U.S. Marine Corps on September 18, 1968
The article does not mention whether he also forged a high school diploma or it was not necessary.
And of course a lot of rebel and guerrilla groups after World War Two have started using teenage and pre teen kids without high school diplomas as soldiers, now that modern assault rifles are so light weight. And it is possible that Heinlein, someone concered about Communist guerrillas, was already aware of that as early as 1958.
As a science fiction writer Heinlein could easily imagine that in some possible futures warfare would be so complex and scientific that nobody could be accepted into the military unless they had a PHD in science and were over 30 years old. But Heinlein didn't intend to write such a story, since Juan Rico and his friend enlisted soon after high school graduation and their eighteenth birthdays.
So clearly Heinlein decided that a high school diploma would be sufficient eduation to be enlisted in his future. Did Heinlein think that a high school diploma would also be necessary for enlistment, or did he imagine a future where educational requirements would still be as low as they were in the 1950s?