I think the thing non-mathematicians and non-CS people who only know complexity theory vaguely need to remember is that complexity theory has nothing to do with reality.

A 2^64bits lookup table only has O(1) lookup if you ignore the impossibility of creating a machine that has 2 exabytes of storage where all those bytes have the same access time. Or you'd have to redefine O(1) to be “at most the worst case”. But strictly speaking from the mathematical definition it’s O(1). Which is why no one in practical engineering takes most complexity results seriously as the entire field maps to practice poorly precisely for these reasons (all our machines use fixed integer math and have limited tape storage)