Certainly don't carry it up. That's the preserve of specialist downhill bikes with extra long travel suspension. More or less impossible to climb hills on them.
But in answer to the question, my current bike has 27 gears, although the latest models have as few as 11 for the very reasons you give and indeed to save weight and complexity. I probably use about half of mine on any kind of regular basis. Very rarely use the lowest of the three main ratios, even when climbing on the rough. I prefer a slower pedalling cadence, by default using more power slowly and rhythmically, as opposed to lots of fast effort to get nowhere. For me, especially as the years advance, my objective is to keep my respiration and heart rate as low as I can so I don't tire too quickly. Relying instead on keeping steady rhythmic power through my legs. Hare and tortoise approach to climbing and save the little remaining energy for the downhill and (only occasionally now!) airborne sections.
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