I think it makes sense to posit something like replicators in TOS.
Consider that "rooms filled with vacuum tubes" in the 1950's were computers, yet only 30 years later desktop computers based on transistors were being mass marketed.
Imagine a few giant replicators on the TOS Enterprise
(which are archaic when compared to the miniaturized TNG replicators) to do the heavy lifting of fabrication. Perhaps the food synthesizers are partially or even totally independent of the fabrication system, and instead more reliant on ecological waste reclamation. If the TOS "fabricators" are big and clunky, then they wouldn't necessarily be used for all the routine recycling tasks.