I'm aware the Nakamura example is old, but the core issue (the horizon effect) is still there in any alpha/beta pruning engine, including the newest SF. But I will certainly grant you that it has become much harder to execute since then.
MCTS engines (like Lc0) are far more immune to the horizon effect, but can instead suffer from missing very shallow tactics, especially in very fast time controls, as Andrew Tang showed in his match against an early version of Lc0 7 years ago:
https://lichess.org/@/lichess/blog/gm-andrew-tang-defends-hu...> Maybe you're right about correspondence chess. That interview is from 2018 and the machines have got distinctly stronger in that time, but 7 years isn't so long and it could be that human input still has some value for CC.
I've played on ICCF and I can say that the draw situation is much worse now, exactly because engines are so much stronger now, so it's much harder to find good opening novelties against a competent opponent.
Engines were infamous for misjudging many closed openings like the KID, but even in the last few years that has really tightened up.
Still, the human element is useful in trying to steer clear of drawish openings and middlegame lines.