Something that isn't entirely clear to me from the video. Do you have to push it from the inside to retrieve it outside? Because that would be super annoying.

How so? The only time you use the lock, you are leaving or entering, and the key forces you to lock the door in order to retrieve the key on the other side.

It would be be better if once I unlock it, the key gets pushed by some mechanical spring, instead of me manually having to push it from the unlocking side to get it on the locking side.

It seems that you can accidentally, or not, lock the door without fully closing it, thus leaving it essentially unlocked, so the key isn’t quite fool-proof.

Some have a lever on the edge of the door preventing the key turning if the door isn't closed

>so the key isn’t quite fool-proof

Yes, it's from another era, when the consumer was not expected to be a fool...

That's one way to describe problematic design. In other words, the key doesn't fulfill its intended purpose considering (as the comment you replied to noted) one can do this either accidentally or not which can have little to do with being a fool.

This key goes to great lengths to make sure the user doesn't lock themselves out. It seems specially designed for 'fools'.