A fairly obvious reason would be to circumvent the treaty with the Klingons. It's rather inevitable that such a treaty would have clauses on how many ships of a given type the two sides could have, and so forth. Pretending that an essentially all-new ship is a "refit" would no doubt allow Starfleet to exploit a loophole of some sort! Or, refitting could be for real, as Starfleet just plain wouldn't be allowed to build another heavy cruiser from keel up and would just have to make the best of the ships it already had - until the right moment came to break the treaty and start the war. Starfleet would feel much happier about starting the war with refitted rather than unrefitted ships...
This is somewhat similar to what happened with the US Navy after the Washington Treaty was signed between the major naval powers of the time in 1922... Prior to the treaty the US was building and commissioning roughly one new battleship a year, but this treaty but the brakes on that in order to avoid a global naval arms race. The US Navy couldn't build any new battleships (and had to decommission or stop construction on a few), but they could refit existing ones. So, during the late 1920s and the 1930's, they ended up refitting a lot of their older battleships, and many of them ended up with a very different external appearance afterwards. The treaty ended up getting discarded during the buildup to WW2 when it became clear that refitting ships wasn't going to cut it any more because the presumed enemy powers were building bigger and heavier ships.