The article deals with the computational efficiency and the simplicity of the implementation of higher order inelastic virtual elements. Compared to the standard FEM, the VEM lacks the simplicity of the derivation of formulas and the simplicity of computer implementation. This becomes particularly problematic when the number of polygons or polyhedral corner points increases, the order of the VEM increases and especially for 3D problems. When applied to nonlinear, path-dependent, coupled problems, such as finite strain plasticity, the computational efficiency regarding the evaluation of the element tangent matrix and the residual increases considerably. In this paper, a fast quadrature compression based on the computation of discrete Leja points by LU factorization is discussed, which for a given accuracy objective reduces the high number of integration points resulting from the decomposition of an arbitrary polyhedron into a union of tetrahedra. The discrete Leja points can be computed for an arbitrarily shaped polyhedron, allowing efficient integration of the consistency part of the VEM tangent matrix and the residual. The introduction of Leja points brings many advantages to the inelastic VEM formulations that the standard FEM-based inelastic formulations do not offer. A 20-node Leja point-based quadratic virtual element has fewer quadrature points than a corresponding 20-node quadratic finite element, making it computationally more efficient than the standard FEM for complex finite strain plasticity models. The VEM mesh can be remeshed with the integration points remaining at the fixed spatial points. The VEM mesh can be locally refined so that it exactly follows the progression of the plastic front. The advantages and disadvantages of the formulation are discussed using characteristic examples.