Why not just do incline or decline push-ups? Or weighted pull ups? I feel like handstand push-ups increase your risk of serious arm nerve compression injuries, like ulnar nerve compression at the wrist.
It feels a lot better(and arguably looks cooler)
I’d imagine flexion also ain’t great to press with, but excessive extension seems to be way more common (and in common push up technique, the norm)
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I already do lots of pushups daily and have for decades, the handstand pushups are just something I enjoy in the morning. It's more how I finish my morning stretches than exercise.
The lots of pushups probably already has my wrists well prepared for the activity.