By "vertical" punching I assume you mean with the palm up ? Lots of gyms teach that, especially when throwing the jab trying to create a different angle. Thats not gonna make a difference what angle your hand is turned, you can still bust a knuckle, twist your wrist, catch your thumb, whatever.
Palm strikes and back handed punches (my favorite) should be practiced as well, but what advantage the boxer gains in a fight is not so much the particular weapon he uses (his fists), but the angles, the footwork/balance, the judgement of distance that are sorely overlooked in other martial arts. Boxing is still tops in many ways.
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