They're valuable to somebody who needs to resupply themselves with food, tools, etc. It's like giving your enemy the keys to one of your supply chains.
But consider this from the Cardassian point of view. They don't really believe they are going away; they have been given the orders, with little warning, but they fully expect to be back next Tuesday. Coming back would be hindered by the new landlords having working shield generators and torpedo launchers. It would not be hindered much by the Feds having working replicators; to the contrary, the more the Feds repair and refurbish, the better when the Central Command again takes over.
We might plead the chaotic nature of the withdrawal, so that only those charged with sabotaging the replicators did their job well, while those responsible for scuttling the shield generators concentrated on looting instead. Or we might say the replicators never were up to Federation standards to begin with, which is why O'Brien has his work cut out for him when everybody complains about already maxed-out hardware...
There's probably a way you can tell official uniforms from replicated by unofficial machine ones.
I sort of doubt there's a way to tell a replicated X from original, for any value of X. I mean, nobody has yet passed a blind test on such a thing.
Perhaps he trusts Garak's tailorly instincts over mathematical precision? He's newly solid and doesn't want to itch or chafe.
Considering how saggy even hero costumes can look on the characters, we may surmise that while replicators can generate absolutely perfect clothing in terms of cloth quality and so forth, they are not the right tools for taking measurements.
I mean, for all we know, Garak replicates all his products, too. It's just that it takes a tailor to
design the product to be replicated, and Garak is the only one accessible to Odo, whereas the Starfleet folks have obtained their sets of measurements from Starfleet tailors (live or machine), to varying degrees of satisfaction, and have no pressing need to go to Garak for new measurements.
Timo Saloniemi