Sure. But going by the evidence presented to us, it simply doesn't seem like Starfleet builds ships with only one stated purpose. Although to be fair, I'm sure a garbage scow isn't going to resemble a Galaxy class starship, but then we've never seen one so who knows? And calling a ship a 'science vessel' is a bit less technical, since we've had at least five different classes of ship which defined that role. If anything, I would call most Starfleet ships 'multi-purpose' rather than a more specific moniker like science vessel, scout ship, battlecruiser, etc.
Heck, the California class is supposed to be a 'second-contact' ship, but there's nothing about it that looks any different from any other Starfleet vessel, or that any other vessel couldn't do that job either.
I will admit that I don't give much credence to non-canon material. And especially not Last Unicorn. They had little understanding of the TNG universe when it came to starships. Their designs were awful, as if the artist was asked to make the ships look like abstract art instead of how they actually looked. And their designs also did not reflect the era in which they were operating.
Don't you mean prequel?