Would the ship even arrive in time were it even used at Earth? Her maximum speed in canon was Warp 5.2 and that was using the mid-22nd century warp scale. Even if the engines on the Refit at the Fleet Museum were some Warp 7 upgrade (hinted at being developed in "TATV...") that's still Warp 7 by the standards of the year 2161. The ship might have to travel several days at high warp to get to the Frontier Day ceremonies and for a 250-year-old starship that may still have 250-year-old engines that might not be a wise idea.
[*Takes off pedant's hat*]
[*Takes off pedant's hat*]