Those are two choices after the engine room.
Even the "bad" (not beneficial) option shows that Joker doesn't WANT to forget about Akechi.

But he has to, right? He wouldn't be able to live with the pain that having this hope for Goro to come back would entail.

I strongly believe that this choice is basically a "Do you have the strenght to still fight? To still hope?" for the protagonist. He says no.

Akira's in pain and already lived through a lot. Goro is one and only person he Failed To Save. And he can't forgive himself now.

Furthermore, it's a scene that determines whether or not you get a Hereward awakening.

If you're able to stay true in your resolve, hope to see Akechi again, stay strong for him and truly, deeply believe in him.

That determines whether or not he awakens to a third persona.

The same happens on 2/2, really.

Akechi needs a proof that Joker can be a support for him.
And if he was able to bear the pain earlier, after the engine room, there's a higher chance he'll be able to do it now too.

Akechi might die. Akira knows this. But even destroying the fake reality he will still believe that Akechi might come back. He already did it once.

He keeps Akechi's glove, even though he should be pretty certain that this is the end.

He should forget about Akechi, but...

If Akechi survived, he wouldn't go find Akira immediately.
We see him with the men in suits. He has unfinished business that he Will Take Care Of.

He knows, even after separation, Akira will be waiting for him. Just as hopeful and strong, because he never forgot their promise.