I'm sure there were economical, personal and practical reasons.
I haven't heard anything to document my speculation, but here goes:
It was 9 years later - Jack Lemmon had aged 9 years as well, so there was no way he would look like "young" Ensign Pulver - keeping in mind the the movie "Ensign Pulver" had a storyline which required it take place within months after the plot of "Mister Roberts".
Jack Lemmon by that time had also blossomed into a major star in the mid-1960s. I'm sure he would not have come cheap.
Also - Lemmon may have had no interest in playing the role that put him on the map, especially knowing how much he had aged/grown since "Mister Roberts."
As for William Powell and James Cagney, they may have been too expensive as well - if they were up to health-wise. Cagney stayed around for many years but he kept his movie profile low, presumably because he had very little interest in making movies. Powell may simply have been too ill, since he was the oldest of the actors you mentioned - and, again keeping in mind the fact that the sequel movie's timeframe is just months after "Mister Roberts," Powell may have looked waaaaay too old to be a functioning naval officer.
"Don't call me 'honey', mac."
"Don't call me 'mac'... HONEY!"
^^That strikes me as a good assessment nycruise.
"Did you make coffee...? Make it!"--Cheyenne.