20-somethings were quite prominent throughout the world's history as commanders, leaders, etc (I hesitate to bring up Alexander the Great, since it is almost a trivial example). The delayed maturity is a product of the late 20th century, and there is no reason for this trend not to be reversed later in the 21st and 22nd centuries. In fact, I actually hope they would be, as the Western distrust and treatment of teens is not something I am comfortable with as an old lady I am.
Now, of course, the history has plenty of examples of the folks in their prime stepping up to the plate to, and even selected for those qualities (see leonidas' Spartans all of which were hand-picked to be old enough to have a son to take over)...
In the end, again, I would not find the age in itself a cause of disbelief, as long as the characters act competently, 22 is as good as 32 or 42 for me.
Plus, due to the nature of spatial exploration, I'd think that younger mission makes more sense due to adaptability and not having roots back at home, etc
While it is true that throughout much of history people who were very young could be placed in major command positions, this was usually because prior to the modern era, the social class you were born into mattered more than merit. Those 20 year old commanders were all royals and nobles. They were also trained from childhood to lead men in both peace and war, so the young Alexander or Julius Caesar wouldn't have been as green as a modern twentysomething, who didn't have a military education as part of their preparation for adulthood.
Even so it's worth noting that men like Alexander or Caesar were very much the exception. For every genius who excelled in their first major command without having risen through the ranks, there was an incompetent disaster of a leader in a similar position who ended up getting his army destroyed. Training alone is no guarantee of skill, and often less important than hands on experience. Some people are natural leaders, but they're very much the exception, and most learn and improve through experience dealing with greater responsibility in gradually increasing steps. A meritocracy allows you to weed out people who aren't suited for higher command before (hopefully) they cause too much trouble. A meritocracy also is better suited to deal with The Peter Principle.
The modern system of promotion through the ranks based on demonstrated competence at each rung on the ladder is far superior to how we used to do things, and much less of a crap shoot when it comes to the end product in high command.
The Alliance or Arkcon going back to how humanity used to do things, by giving inexperienced 20 year olds major command responsibilities, would be a major step backwards. If the universe were real and not a the invention of video game writers, it would also be a recipe for eventual disaster. The first time that organization runs into hostile aliens at a technological parity, who promote through a meritocracy, the humans are probably going to get trounced.