Phase space theory (PST) is applied to the calculation of state-resolved integral and differential cross sections for the complex-forming atom-diatom insertion reactions A + H-2 -> AH(2) -> AH + H with A = C(D-1), S(D-1), O(D-1), and N(D-2). In the asymptotic channels, vibration motion is quantized while rotation and translation motions are treated classically. The approach is compared to exact quantum scattering calculations and quantum statistical models. Given the simplicity of PST, the agreement with the previous much more refined treatments is very satisfying. Although PST is a well-established theory, this work is, to our knowledge, the first such systematic comparison of its predictions with accurate quantum scattering and quantum statistical calculations.