I was always of the understanding that it was a mid range exploration ship, almost a hybrid of Galaxy class and smaller science vessels.
A couple of things point me to this conclusion.
1) Janeway as Captain.
She had a science background, it seems appropriate to think that her ship would have been related more to science than deep space exploration, battle, patrol or diplomacy.
2) Lack of resources.
Now although Voyager did not expect to end up in the Delta Quadrant, it's unlikely it would have been pressed into service, undertaken the journey to DS9 and then go looking for Marquis in a dangerous area of space without full resources. However very early into the Delta Quadrant they begin to run out of resources.
This is in contrast to say a Galaxy Class starship which carried far more personnel, equipment, facilities and resources, and is designed to be largely self-sufficient.
My point is, I am confused about the purpose of the ship, It didn't "really" seem to be built for battle (Struggling with primitive Kazon and other species, not present in Dominion war).
To me, it was never made clear, and seemed to just be "given" abilities to suit the story, at times being an impressive battleship, at others being well suited to science.
What is your take on it?
What is the Intrepid class actually designed to do?