We have been saying it in writing and podcasts for years, the hip flexors are limb swing phase PERPETUATORS, not initiators of hip flexion.
It is the elastic response discussed below and the changing of the pelvis obliquity (from posterior positioning to anterior) via the abdominal wall acting on the pelvis-hip interval in conjunction with the stance phase hip musculature that drives hip flexion.
The next time you go after the psoas as a culprit in your meanderings for solutions, because that is what is all over the internet, think bigger, smarter, deeper.
"These experiments also showed that the trailing leg is brought forward during the swing phase without activity in the flexor muscles about the hip joint. This was verified by the absence of EMG activity in the iliacus muscle measured by intramuscular wire electrodes. Instead the strong ligaments restricting hip joint extension are stretched during the first half of the swing phase thereby storing elastic energy, which is released during the last half of the stance phase and accelerating the leg into the swing phase. This is considered an important energy conserving feature of human walking."
Dan Med J. 2014 Apr;61(4):B4823.
Contributions to the understanding of gait control.