Ange's words made Anthony's head explode with a bang, and he suddenly realized he had overlooked a crucial issue.
Due to preconceived notions, when the Gate of No Boundary mentioned the Endless Cage, he naturally assumed that the Endless Cage was the Boundless Space Hole. Since they had already escaped from the Boundless Space Hole, it was equivalent to being free of the Endless Cage, so they didn't need the key.
But here's the question: why is this 'key' outside the 'door'? If it was the only key to escape the Endless Cage, why would it be outside the Boundless Space Hole?
You have a cell key, but threw it outside the cell, does that make sense? Waiting for someone outside to open it for you?
Logically, it doesn't add up, and the doorknob said it was 'your only key to leave the Endless Cage', not 'the key to enter' the Endless Cage.
If we think differently, if this place is still the Endless Cage, then the logic fits.