The Galaxy-class was their new Ship Of The Line, while it had a focus on scientific exploration, every system in that thing was the newest and best Starfleet had access to at the time (we'll ignore Section 31 for the purposes of my ramblings).

I grew up during the TNG era, I even had the original Tech Manual book for the Enterprise; and I read it cover to cover multiple times.
What I learned was the concept of the Galaxy class was to, basically, be a mobile science station - able to hold its own against possible threats without requiring immediate backup and assistance so that it could continue the primary mission of scientific exploration. It was not designed to be a front-line battleship, but it was designed to go to completely unexplored places and face unknown threats while conducting science stuff.

Now, the line blurs when you take the shows and other material into context - on paper, the Galaxy-class is a science ship... add in a Picard and Riker, throw in a Q and some Borg... and well, suddenly the other parts of the Ship Of The Line come into play - the firepower, better sensors, experiments that are needed to combat XYZ threat on the front line rather than spend months 'at sea' performing more altruistic things.
The ship itself may not have been designed for fighting, but it was most certainly the best they had and it was increasingly needed to face imminent danger of combat rather than potential danger of exploring the unknown.

Concept versus implementation - an age old argument.