When the queens are off the board, the king is better in the center.
When the queens are still on the board, the king is better castled.
Gaining positional advantage without castle king
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It's not because he castled. It's because you were better from the very beginning and never lost the advantage.
Many players do not know the fact that when the one keeps the king at center, he will gain positional advantage if most of pieces are traded off and eventually win the endgame.
Here are one of the most recent game that I played:
I played this game as black. It was a 10 mins rapid game with my elo about 2020 and opponent elo about 2120. I gained the positional advantage without castle king and traded most pieces, making to knight vs bishop endgame. The materials were equal with each sides having 7 pawns. However, my king was at center file and opponent's king was at flank file. After that, I walked up the king to center than beyond the center and eventually won the opponent's pawn to win the game. (According to stockfish, I dominate the game through the whole game)
Thus, this game is a very good demonstration why the one should not castle king to avoid of losing the game in long term.