Noway, Doomsday plays in a different league, he adapts, even if he is not damaged, the simple reason why it's not possible to materialize in the phantom zone, is a harm to his former reality.

Superman and Doomsday are well-matched in terms of physical prowess, but when it comes to adaptation, no, adaptation is the way how Doomsday progress, because he can't learn, he can't rationalize, he's pure instinct, while Superman has to develop his powers through experience, therefore intellectually gain a major focus over his powers and learn about himself and his Kryptonian nature, unlock new ways how to boost himself furthermore.

Why did you bring up Doomsday?

Because, he can perform feats, where reason is a none-factor, there are certain situations where rationalization won't give you some progress, Doomsday could only escape because every tiny cell and how his mind work is some sort of an instinctive quantum calculator without emotions, but destruction, that's why at some point, he developed an antibody against the Phantom Zone, so that he returns to his former reality.

My thread is about Superman's ability to destroy the Phantom Zone

Exactly, for the simple reason, Superman relies on rationalization, it's not possible for him to escape.

Eh, it doesn’t really say how exactly he could do it or how long it would take him. I really like that art though.

Read issue 2 then issue 5 the phantom zone in the story is a pocket universe