Bike Anti-Porn - When Things Go Wrong

^^ I don't see why both positions couldn't work: you lean forward to ride the bullhorn, move upright to ride the other part.
What's not to work?
Anyway, we're arguing internet pics here, none of us (presumably) have tried this combo.

The biggest downside is too many hand position.

Ideally you want to have a decent contact point where it's not too stretched or upright, with a little bit of error room (e.g. on drop bar, flat section for upright, hood for normal, drop for aero as fuck).

If you put a huge amount of hand position, it would take quite a while to get used to it, potentially never, and affect your positioning too, more upright bike may need a saddle nose pointed up more, whether a stretched out bike would required the saddle to be levelled, or almost so.

The German Lesbian Handlebar (AKA butterfly) is one example.