The contradiction of the Enterprise D mission role.

[cgervasi]

So if the Galaxy Class really intended to be an exploration ship, why would a Hegemony Empire like Federation send their best assets to far far away from home just to explore some uncharted space, while at the same time they have only smaller, less capable ships like the old Miranda and Excelsior to protect their home?

I think the Galaxy class is designed for deep space exploration, so it has to have the best scientific facilities and the best defense systems because they don't know what they are going to encounter.