Real life explanation:
The main cast members are all officers, so they are the ones who are doing pretty much everything in the shows. Except for a few background extras who pretty much are only there to get killed. IF they were using specialized boarding parties they would be A: The new main characters, that would either bloat the cast giving all characters reduced screen time or B: Their actions would be mainly off-screen or short cutaways with some nameless grunts.
In Universe Explanation:
Starfleet is not a military organization but more of a police force. That's why they don't have marines on their ship. At best a ship is only housing a small security force and that's it. The Defiant for example, a war ship was classified as an Escort Vessel because of the ideology that warships don't belong in the Federation.
The last real military branch part of Starfleet were the MACO's, but they were disbanded at the founding of the Federation with the remaining officers taking new positions in the Federation.
I admit it's ridiculous at times, like in an episode of DS9 where three two-person vessels were used in combat by the head of the station, the second in command, the chief science officer, the chief engineer, the chief medical officer and head of security while there were dozens of Bajoran and Starfleet personnel available.
It was rule to always have a senior officer present for negotiating purposes as Federation policy was to avoid conflict. It was advised that captains do not join the Away team (something Janeway and Picard rarely did), but Kirk, for example, loved the excitement of going in head first. The reason why there is often more then one officer in the away team is because of the need for medical/engineering aid, or something technical/scientific that needed to be researched by the chief engineer/science officer. In reality, those are just excuses to solve the real-life issue of keeping the cast size to a minimum.