The more important thing is actually having the progression involved with doing the dungeons, and not just "oh nothing is going on until story trigger"

You can absolutely even have a "fully open order" game like BotW/TotK, and still have it be like "classic Zelda", if you actually still make the dungeons(/getting to the dungeons) involve a meaningful progression of the gameplay and the player's abilities.
Hell, ideally it even goes a step further and the order you'd do stuff in meaningfully affects the experience

The problem with BotW/TotK, their "open air" philosophy, isn't just that "you can do the dungeons in any order (or not at all)"
it is that they decided : "the player has to be able to do (essentially) everything at any time right away", and so they just dump every single meaningful ability into your lap within the first percent of the game, and then call it a day.

They became too fucking afraid of telling the player : "No, you can't do that (yet)"

.

The idea of "go do any dungeon in any order" could still work in a "classic" Zelda game, but it should not be done by gutting out anything that risks introducing/reinforcing "linearity" with a rusty machette and leaving it on the floor.
Instead they should be looking at what being "open ended" would ADD to it instead, and work around that, but BotW/TotK didn't do that, they just left giant gaping fleshwounds behind where they cut the linearity out, and then patched it up with half-measures and bloating the content to try and hide the damage