Another example to illustrate the point is the ICCF (International Correspondence Chess Federation). Were computers comparably competent at long-term play as they are at short-term, then there wouldn't even be a competition. It'd simply be who has the strongest computer. But in reality that seems to play no particularly decisive factor. For instance, as in "normal" chess, there remains a huge gender divide in ratings, yet females certainly have no less access to competent hardware than males.
Chess, for a stronger player, is very much like a language - in fact it uses the exact same area of the brain. It's like when you read these words, you're not consciously thinking at all - the meaning just comes to you immediately. And in fact you could trivially recall everything I said (even if not necessarily verbatim) if you just thought for a second or so. But simultaneously it's not like you actually made any effort whatsoever to memorize it.
So how long of a conversation could you hold with yourself in your mind? Practically endless, and you could probably reconstruct the overwhelming majority of it on demand. It's the same with chess. Meandering around in your mind to positions of an arbitrary depth is not difficult for a strong player. And the person I was responding to felt that a player writing down some analysis to move 20 would be some meaningful form of cheating. In reality, I'd absolutely love for my opponent to be able to write down their analyses. It'd waste just a monumental amount of time and afford no advantage whatsoever. It'd be akin to you writing down the conversation from your mind.
How are these points connected? Playing blindfolded doesn’t require being able to calculate 30 moves deep (or any particular number).
Being able to remember/visualize an N move sequence without losing the thread while blindfolded is not at all the same thing as being able to calculate N moves deep.