The three main uses of the Reliant studio model in TNG and DS9 were the Lantree, the Brattain, and the Saratoga. For the first ship, it was quite clear that it was an old ship relegated to transport duty. However, the Brattain was a science vessel and the Saratoga was a ship-of-the-line, both clearly on active duty. All three uses of the model were predicated on them not wanting to spend money building a new transport ship, science vessel, or other new ship of the line. And because the filming model lasted long enough to be scanned into a CGI model, it then appeared a multitude of times in DS9 and VOY as generic Starfleet vessels. But I don't think they outlived their potential replacements. As I mentioned above, they were just generic ships that we happened to see a lot of during wartime because, well, that's what we happened to see at the time. We would have to imagine that other battles we didn't see contained other classes of ships that were not composed predominantly of Excelsiors and Mirandas.