If, from your perspective, a Zelda game distinguishes itself primarily by how good of a puzzle delivery platform it is, then sure, larger scale puzzles beyond the scope of a single shrine are sort of absent from the “of the Wild” era games. I suspect this was a conscious design decision, because once a player has to hold significant state in their head, any interruption (this is a mobile console after all) will lead to a number of players being stumped and not completing the game. The same idea applies to tasks with multiple solutions, funneling players by only allowing one solution, one path through the game will mostly just lead to gatekeeping and exclusion. You can see that kind of thinking exemplified in the design of the TotK dungeons, each of which are basically half a dozen independent puzzles leading up to some unrelated boss fight.
Personally, to me puzzles are a fun diversion and not very important at all. What the original Zelda was amazing for was its hardcore exploration. After being more and more limited and railroaded in LttP, then LA, OoT went too far for me. It never clicked for me, even after trying several times, and I left the franchise basically until BotW, with exploration once again being front and center of the Zelda experience.
I agree that everything after LA and before BotW could have been its own franchise. But BotW is more “Zelda” than basically every other Zelda before it, and I’m happy it has returned the franchise to its original, “proper” form.
With Genshin being as popular as it is, expect the next Zelda to become a Gacha-fueled live service game, with drip-fed narrative and piecemeal dungeons.
As long as that doesn’t happen, I’d say we’re still okay.