Here’s my explanation for why senior officers always go on away missions.
We don’t get to see much of life on Earth or other planets in Star Trek. We are given to understand that it is pretty much a utopia. We are also told (sometimes) that there is no money, at least by the time of TNG, and Kirk denies having money in The Voyage Home (though arguably he only means cash). People are generally shown to work not for financial gain but for self-improvement. But utopias are boring. Self-improvement is boring. What clearly motivates the people in Star Fleet is adventure. Senior officers are basically administrators. Paperwork and staff meetings aren’t exactly going to satisfy anyone’s need for self-actualization. Without monetary payment why would anyone want to be a captain or a first officer? Because that’s where the action is! Star Fleet discourages starship captains from leading away teams, but they know they can’t actually do anything about it because that is how captains are rewarded - they get to choose the away teams, and as much as possible they choose themselves! Starships clearly have boring duty assignments - characters sometimes complain about them, Captain Picard once called Turbolift control for crying out loud! What a boring job! Why would anyone do it? In the desperate hope that maybe, just maybe, they will someday be promoted to a position that gets to actually beam down to an alien planet just once, even if it’s just as a red shirt to be fodder for the tar pit alien of the week!
It’s often been commented on that most of what Star Fleet does doesn’t even need people! Why not just send down a probe to do reconnaissance? Why send an entire starship to go explore strange new worlds when it could be done much more easily from home? Why are the same five people sent down to explore an entire planet when they get there? Because the only thing that gets people to show up for work at all in Star Trek is the opportunity to do something actually dangerous and exciting now and then! And those opportunities are kept artificially scarce in order to preserve the value of the only currency Star Fleet has available.