I don't think Goro can get rid of Shido's palace on his own. One of the reasons why Futaba was so pivotal to the arc is because i firmly believe (going from the beloved dante inspiration that the series loves to dance in) that humility is needed to defeat pride, something that Goro, as a character, would definitely struggle with at this point.

Humility to accept help, to accept you're own weaknesses and flaws. I don't think Goro would survive in there on his own and if Ren was arrested in his place, Shido might have had another officer kill him in prison if he doesn't find a way to escape.

MORE FUN and more likely is that if Goro goes missing in Shdo's palace and Ren somehow manages to dodge being arrested by Sae. He'll go to the Phantom Thieves for help and join them for real, if only, because he knows this is more than he can chew, but no matter what, it'd be too late for Goro, it's just a matter of whether it'd be too late for Ren too.

After all, Cog Goro would still be a problem lmao.

Cognitive distortions are a real term in psychology! :3 A definition for example is "A cognitive distortion is an exaggerated or irrational thought pattern involved in the onset or perpetuation of psychopathological states, such as depression and anxiety. Cognitive distortions are thoughts that cause individuals to perceive reality inaccurately"

The key word here is to perceive reality inaccurately It's not about negative thoughts or actions per say but rather involves your entire perception of your reality being warped in a twisted way. You don't have to have a distorted view of reality of your actions and their impact to commit evil deeds. Which is how I'm glad that ultimately in canon, Akechi doesn't have a palace. He doesn't have a warped perception of reality, he's well aware what he's doing is wrong, he doesn't delude himself about the kind of person he is, and his circumstances. He accepts them. Every negative part of himself, his thoughts and his circumstances and he looks it dead in the face.

People like Kamoshida or like Shido, see the world in a particular view point wholly divorced from reality of their circumstances.

In the real world cognitive distortions apply to things like extreme depression and anxiety hence why people like Ren and Futaba can end up with palaces due to extreme levels of depression that cause them to view their reality different.

Especially in the context of the world of persona where people who escape the mementos depths do so to avoid living under society's whim of being controlled and having their lives decided for them. There's an element of 'i want control over my circumstances, and this is how I keep it, via this distorted reality'

They quite literally live in their own bubble. It's fascinating! These feelings are things everyone has and struggles with hence why almost everyone has a shadow in Mementos, but i believe when those feelings become so strong they feed into those "seed of a treasure" that Morgana references when they took the first person's treasure in mementos and when those seeds are sufficiently watered with toxic emotions and distortions they bloom into a palace.

If the sin that defines them grows out of control then I believe that's what spawns palaces. :3 BUT thank you for this question it was great to ramble. I hope I made sense!

But yea, Ren accepted himself by rejecting his sin, his sin of treachery, the sin that he betrayed himself by not being able to help Shiho, and vowed to always follow his heart no matter what it may lead. Hence why he's not distorted despite him being very much still depressed lmao.