While that may work for a few months - eventually you can't add that much weight to your back and it is absolutely horrible for your posture so you risk injury by even trying to put it on
there’s only so much progressive overloading you can do in a short time. My chest workout is about an hour long and I jump from 135 pounds to 350 pounds during my workout. It would take 100s of push-up reps to get the equivalent of that.
Yeah, I'm not arguing that PU overload is more efficient than bench overload, I'm just saying it's possible.
It will hurt your posture long term, no doubt , but benching isn't any less harmful to your body long term, or less risk averse.
Another reason weighted PUs are good, is it's a more practical stress activity. In other words, you'll find yourself in situations where you have to carry something heavy and move around aggressively (military). You may have to climb over a wall with a ruck (I use the same ruck to do pull ups, chin ups, dips, and sprints). I'm ex Army, so I prefer activities that resemble practical use in a dire situation.
I bench too, not against it. I think a balance between calisthenics and resistance/weight training is key to an A1 routine.