Just because food can be synthesized, doesn't mean it won't need to be cooked and prepared. When you buy synthesized meat you still have to cook it.This is a really convincing argument- but how do we reconcile the fact that in Star Trek: The Undiscovered Country, we clearly see a fully operational kitchen, where people are making things with ingredients? There is also what appears to be a frozen turkey sitting out on a countertop. If it were possible to replicate or 3D print food, why would they need an entire turkey? Let alone individual ingredients? You could just print out the whole dinner and be done with it.
There's a lot of skill, artistry, fun and even a ritualistic aspect to food preparation. People like doing it so there's no reason to think chefs and kitchens will go away because of synthesized food.
On TNG they still play classical instruments and read books. People today do lots of things that tech has made obsolete.
But I like your idea in theory. Trek needs to be the future but still tie itself to the problems, tech and science of today so it can explore contemporary issues. Sort of like how the Orville had an episode dealing with social media.