  We use $\vec{k}\cdot\vec{p}$ theory to estimate the Rashba spin-orbit
coupling (SOC) in large semiconductor nanowires. We specifically investigate
GaAs- and InSb-based devices with different gate configurations to control
symmetry and localization of the electron charge density. We explore
gate-controlled SOC for wires of different size and doping, and we show that in
high carrier density SOC has a non-linear electric field susceptibility, due to
large reshaping of the quantum states. We analyze recent experiments with InSb
nanowires in light of our calculations. Good agreement is found with SOC
coefficients reported in Phys. Rev.B 91, 201413(R) (2015), but not with the
much larger values reported in Nat Commun., 8, 478 (2017). We discuss possible
origins of this discrepancy.
