Though note that, despite what Discovery thinks, they didn't have replicators in Kirk's time. Food was prepared in the galley and distributed through the food dispensers in the mess hall.
Even the Enterprise-A still had a practical galley.
In TOS, the Enterprise had some kind of rudimentary food synthesizers, but they made these:
At least I hope to God those abominations weren't made by someone in a kitchen somewhere in the underbelly of the ship. Our astronauts eat better than that, even today.
By the time we see the galley on the Enterprise-A in The Undiscovered Country, it was probably mostly there for special occasions or diplomatic functions. Even in the TNG era, when replicators are very nearly perfect and can create any kind of food you might imagine, traditionally prepared food still seems to be seen by many as a cut above, or premium option.
The NX-01 definitely had a proper kitchen and their setup was much more like a cafeteria, with things constantly being prepared and then transferred to those storage slots in the mess hall for people to take. I also thought it was kind of a neat, if antiquated, touch that Archer had his meals specially prepared by the head Chef.