Personally, I've always thought that Starfleet built explorers with teeth - i.e, their primary mission was to explore, but they were also heavily armed enough to be a match for comparably-sized vessels (with the exception of dedicated science vessels like the Oberth-class). I don't think Starfleet would officially classify any of their ships as warships - even the Defiant is officially classed as an "escort" because, as Kira says in 'The Search' - Starfleet doesn't believe in warships. It's possible the Dominion war, and the recomissioning of the Defiant class into production has changed things, however I can see Starfleet wanting to get back to their exploratory roots following the Dominion war - such as in the Titan novels etc
Agreed. I do think that perhaps there are a handful of designs, like the dreadnoughts and the Defiant, which might be considered to be true dedicated warships. But many of the sources I've read which have included such vessels have described them as being a minority of vessels, given the increased resource costs and the fact that they tend to be less suitable for more traditional roles like exploration. I think the majority of designs we see are multipurpose, as is probably true of many alien ships as well.
Although they can double up for scientific missions, The Constitution and Excelsior-class must have been considered primarily warships as in Star Trek VI: The Undiscovered Country when they are discussing peace with the Klingons, one officer asks "are we talking about mothballing the fleet?"
The Excelsior was considered a battleship in the FASA RPG, and I think it could have easily been built as such initially and then perhaps downgraded to a heavy cruiser, as it's referred to in other sources. It was intended initially to be able to face threats from the Klingons and Romulans in the movie era.
