The validity of quasilinear (QL) theory describing the weak warm beam–plasma instability has been a controversial topic for several decades. This issue is tackled anew, both analytically and by numerical simulations which benefit from the power of modern computers and from the development in the last decade of Vlasov codes endowed with both accuracy and weak numerical diffusion. Self-consistent numerical simulations within the Vlasov-wave description show that QL theory remains valid in the strong chaotic diffusion regime. However, there is a non-QL regime before saturation, which confirms previous analytical work and numerical simulation, but contradicts another analytical work. We show analytically the absence of mode coupling in the saturation regime of the instability where a plateau is present in the tail of the particle distribution function. This invalidates several analytical works trying to prove or to contradict the validity of QL theory in the strongly nonlinear regime of the weak warm beam–plasma instability.