I didn't click on the link. But if you are referring to the 4-year cycle pattern, that's very familiar. Did you really find it yourself?
Anyway, what happened in the past may or may not happen again. It is not in any way a guarantee that it will happen again. If it happened once, twice, thrice, that still doesn't assure you that it will happen again. So I wouldn't go all-in on that.
Perhaps the only thing that I'd like to believe as a guarantee is that better days will come. Whether it will follow the 4-year cycle pattern or not, it doesn't matter. What matters is that we will make another ATH sooner or later. That's something I can bet all-in.
You are right and I believe this should be the main focus of most investors and not how soon the next ATH will be. History has shown us that Bitcoin has been able to recover after every bear market and whether it repeats this after every 4 years like before can't really be confirmed as you said but at least from the general BTC price trend so far, it has been on an upward trend.
Why won't btc record another ath after the next coming halving? I don't think this is even a question to be debating on, looking back at previous circles already shows what will happen after the next halving. The only thing no one can guess right is how high the next ath will be.
There have been more advancements in the area of acceptance and adoption which is an additional push toward btc widespread all over the world in the different economic sectors. The pattern may not be the same but btc will definitely record a new ath, there is no other coin like btc, don't forget that.