This paper explores the benefits of utilizing multistage cascaded (CC) behavioral models for digital predistortion (DPD) linearization of wideband high-efficiency power amplifiers (PAs). To reduce the computational complexity of these multistage CC behavioral models, a model-order reduction technique based on a greedy algorithm is proposed. The advantages of employing CC DPD models with gradient descent parameter identification, as opposed to single-stage DPD models with least squares parameter identification, are extensively demonstrated and analyzed. The trade-off among linearity, power efficiency and computational complexity is evaluated considering the linearization of a high-efficiency pseudo-Doherty load-modulated balanced amplifier (PD-LMBA). Using the proposed pruning strategy for CC DPD models, we demonstrate a significant reduction in the number of parameters needed to linearize the PD-LMBA. The PA operates at an RF frequency of 2 GHz and delivers a mean output power of 40 dBm with an approximately 50% power efficiency when driven by 5G new radio signals with up to 200 MHz bandwidth and an 8 dB peak-to-average power ratio.