Replicators have been cited as the invention that allowed humans to stop working for a living. This implies that replicators are cheap and even free because they produce food at super-low cost. So low that humans can stop work. However, if replicators are indeed so low-cost, why were they shut down in the Voyager? Cooking replaced replicators in the Voyager. This implies that replicators are more expensive than manual cooking. If so, how can replicators give humans the luxury to stop working?
The lack of ready supplies of energy is a constant feature of the first season of Voyager. Limiting the use of secondary systems like the replicators (and their rationing) was a good way of showing this to audiences.
KIM: There's an ancient Chinese curse, Captain. May you live in interesting times. Mealtime is always interesting now that Neelix is in the kitchen.
JANEWAY: We shouldn't judge him too harshly. He is helping us conserve replicator energy.
NEELIX: You're welcome. After all, if you want the crew to begin to accept natural food alternatives instead of futher depleting our energy reserves, you need to encourage them by your own choices, don't you?
JANEWAY: Fine. Give me your even better than coffee substitute.
Now, you might ask how much energy these systems actually use. We learn in Dark Frontier that their continued functioning equates to entire light-years of travel for a Starfleet vessel.
MAGNUS: We have to keep moving. If we take the replicators offline and run environmental systems at half power, we can go another twenty light years before refuelling.
The answers I've seen here are an excellent exploration of the first part of your question, namely, why were the replicators shut down on Voyager.
However, what I'm not seeing are any answers to the second part of your question, namely, if replicators use more energy than cooking, then why did they allow humans to stop working for a living? Wouldn't the increased energy cost imply that replicators themselves were not a good substitute for manual labor?
If I may rephrase the question in modern parlance, it seems that a similar question would be "how did thousand-pound vehicles replace walking and horses and buggies, which are much lighter and therefore energy-cheaper to operate?" The answer to this question is, of course, plentiful gasoline.
I'm no Trek loremaster, but it would seem to me that we would have to posit the existence of some huge, abundant, cheap supply of energy to allow the more-expensive replicators to replace the less-expensive humans. The warp coil seems to be a convenient mechanism to explain precisely how replicators replaced human manufacturing labor, though I have nothing to quote on this.
The Enterprise and most Federation ships seem to never be more than a few weeks away from a Federation outpost where it can top up.
Voyager is 70 years at maximum warp away from the Federation and has no established logistic support system - they might be able to trade with Delta Quadrant civilisations - but there's no guarantee they can get the right fuel. Food, on the other hand, seems fairly universal (although of questionable palatability).
The problem was the energy cost. Energy in the federation is abudant. But as the voyager was far from home it had to rely on dwindling sources of energy....which meant replicators became a luxury and thus had to be reduced in usage as their energy cost was enrmous.