On the other hand, I find its immediate replacement to be appropriate: there's only so much time that can be spent caring about a warship in a conflict like this.
Some have said that replacing it undercuts what previously happened, but I don't think it really does. The attachment the characters might have to the old Defiant is based on the experiences they shared on it, not its "uniqueness" as a machine. Also, it's just a ship. Let's not get carried away.
Replacing the Defiant makes sense, but they replaced the Defiant with another Defiant class ship which they then renamed Defiant and gave the ship the Defiant's exact registry number. I understand why they did all that for budgetary reasons, and at least they changed some of the colours on the bridge, but it was a little underwhelming. It would be like replacing Jadzia with Jadzia's identical twin sister who is also called Jadzia.
I don't have a problem with it. The new Defiant was meant to be the Defiant A and if by some miracle the new Defiant is ever seen again on film, it will almost certainly be identified as the Defiant A. Perhaps this will happen if DS9 is remastered.