From what we have seen in canon, it is supposedly a huge moment when a Captain recieves their first command, or a new ship, and this music conveys the emotion tied to that.

But is this really a larger issue within the game, in that, our ships are NOT special, and we seem to toss them away with impunity, rather quickly, for most of our "careers"? It's like our ship is nothing more than a piece of armor that gets scrapped as soon as a better piece is found or made available.

Simply put, this game fails in establishing the importance of our ships, and making them important to us in the same manner that the ship was important to Kirk, or later on, to Sisko (when he lost the Defiant).

However, adding a cutscene and music, isn't likely to fix this issue, when you gain a new ship every few hours, and your previous ship becomes quickly forgotten.