Almost all necks flex a little under string tension, and those necks need an adjustable truss rod.
It is possible to build the neck stiff enough that there is no measureable flex from string tension, either with steel or carbon fiber reinforcement. The relief would have to be built into the fretboard/frets, and would not change with changes in string gauges. I've been thinking of building one like this, but all my builds so far have had double action truss rods.
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Rodger Knox, PE
1917 Martin 0-28
1956 Gibson J-50
et al
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