Similar to If everyone uses replicator, why do tailors still exist?, why is Neelix almost always cooking when we visit the officer's mess? Surely the replicator can produce any known recipe it has been programmed to? Or is Neelix cooking new recipes, to then program the replicator for?
Replicators use Dilithium, which was scarce
Every use of the replicator takes energy:
A replicator, replicator system, replication system, or molecular synthesizer was a device that used matter-energy conversion technology similar to a transporter to produce almost anything from a ship's replicator reserves. (TNG: "Lonely Among Us", "Deja Q"; DS9: "Visionary"; VOY: "Virtuoso"; ENT: "Dead Stop")
— Memory Alpha
Because Voyager was low on that energy, Janeway implemented rationing:
After the USS Voyager was pulled to the Delta Quadrant in 2371, an energy crisis occurred several weeks into the journey back to the Alpha Quadrant, and Janeway ordered replicator usage to be rationed in order to conserve power for other key systems. These replicator rations became a type of currency among its crew. (VOY: "The Cloud")
— Memory Alpha
Neelix was able to cook with most of the plants native to the Delta quadrant, obviating the need to use replicators and thus letting crew members eat without having to use rationed resources or spending their replicator 'currency' elsewhere.
A couple of reasons:
- Replicators have been stated multiple times as being inferior by most measures of quality to a real cook. It’s never clearly explained why, but the implication is that it’s similar to the difference in real life between mass-produced fast food and a hand cooked family meal made from scratch. It’s worth noting that Neelix is not the only conventional cook we see throughout the various series (off the top of my head, Joseph Sisko is the master chef of his own restaurant), and this is implied to be a key reason why people still cook.
- It’s implied a couple of times throughout the various series that programming a replicator is at least as difficult as producing whatever the replicator is being programmed to produce by other means. This probably partially feeds into the above point, but is worth mentioning on it’s own, because it does not appear that there is some fancy molecular gastronomy simulation package in universe that could translate a traditional recipe into a replicator program to produce the same food. In effect, this means that the crew of Voyager was otherwise stuck with whatever was already programmed into the replicator at the start of the voyage, and even with a rather broad menu eating the same things all the time gets boring after a while (which in turn is bad for morale).
- Replicators still require power to work, and Voyager had a limited power budget throughout most of it’s trip through the Delta Quadrant. Rationing of replicator usage was implemented early on, and is mentioned multiple times throughout the series. In that situation, I for one would very much welcome another option for daily sustenance, because it would mean I could spend my replicator rations on other things. This is compounded by the fact that replicator technology is not perfectly efficient (that is, it produces less matter than the amount of energy input would imply if all of that energy were converted with perfect efficiency into matter), which means that even recycling of waste matter could not eliminate the power budget issue, just mitigate it.
- Neelix wants to help, but he’s implied to be at best mediocre at most of the technical jobs that would be needed to run a starship (even ignoring the issue of a Starfleet vessel being completely different in many respects from the ships he’s used to dealing with). He is, however, a good cook, and this is something that none of the rest of the crew seems to be interested in doing, so it’s a logical job for him to pick up, especially since he already has experience dealing with the ingredients available in the Delta Quadrant.
Edit in response to comments requesting citations for the point about replicators requiring feedstock:
On further inspection, I have now realized that my point about the requirement for feedstock for the replicators was based solely on information from non-canon (albeit properly licensed) sources, and I have thus removed this point from the original answer.
However, looking into this has made me realized that I could actually further expand on the point about the power budget (because there are multiple canonical references implying that the matter-energy conversion used in replicator technology is not 100% efficient (most prominently a comment by Spock about the titular weapon in TAS S1E14 ‘The Slaver Weapon’, which also relies on matter-energy conversion)), and I have expanded that point accordingly.
Because they're growing their own food
Replicators are very energy-intensive and a major drain on Voyager's limited resources.
One of the cargo bays was converted into a hydroponics/airponics bay to grow fresh food fairly early on.
I have to assume that keeping grow-lamps on and running the hydroponics-pumps is less energy-intensive than fabricating food via teleporter.
Aside from that, they were known to have traded for fresh vegetables which they stored in the cargo holds (I have to assume either frozen or in stasis-fields to preserve them long-term)
The upshot is that when you have a vegetable in hand, you need a cook to prepare it into food, the replicator can't do that for you.
Puzzlingly, most mentions of the Airponics bay refer to them growing decorative (non-edible) flowers.
Apparently they were growing food efficiently enough there that they had room to spare for "just-for-fun" projects like gladiolas and chrysanthemums.
Similar answer to your link: sometimes the replicator is still not programmed for certain recipes, but mostly it's for the simple joy of cooking. And probably some would complain that "food from the replicator doesn't taste like the real thing".
As described on Memory Alpha:
Neelix was an enthusiastic cook and ran the ship's mess hall. He was fond of experimenting and often tried to adapt crew members' recipes with the limited ingredients available in the Delta Quadrant, although they often complained about the results. Early on, Tom Paris remarked that Neelix's cooking was "always interesting" and the glutinous "Even better than coffee substitute" Neelix developed from native plants strongly motivated Janeway to seek new sources of energy for the ship so that she could use the replicator guilt-free. (VOY: "The Cloud") However, he was able to successfully cook a blood pie for B'Elanna. (VOY: "Day of Honor") He enjoyed finding new ingredients to work with, which usually took the form of produce rather than meat. (VOY: "Random Thoughts")
Voyagers case, it's lightyears between various stars and features which have access to it's most prized source... Deuterium. With only 1 out of every 6500 hydrogen atoms in abundance.protium-protium fusion does work (the sun). A ship at warp takes weeks to cover a single sector, in any situation fuel supply could be exhausted before refueling was sufficient. starShips in friendly space are refueled at ports or fuel containing starships...also the biggest aspect, anti-matter and dilithium.
Replication is an acceptable crutch, because it's alot better than the volume needs of a 150 person, multi-racial crew with different food desires, to carry foodstuffs....Growing food is more energy efficient but more time consuming. The amount of energy to replicate is very substantial, They do it not because it's energy efficient but volume efficient. Carrying enough food to sustain a crew of 150 for 1 year would consume a modest amount of space, Tack on culinary demands and diverse menu options (Chicken, pork, beef, etc) not to mention alien species, volume demands grow 10 fold.