You mention TOTK and I assume by extension BOTW. Let's suppose you built these games to have no load screens, what would it look like?

Every shrine you open must have its entire level geometry loaded into memory as you approach it.* And the shrines in TOTK have that weird "bag of holding" trick, where the interior space is larger than the exterior shape would allow. In game and in real life, this is a camera trick, it's an optical illusion to make the entrance look larger than it is. But it's not a camera trick anymore, it's the actual space. How do you load the entire shrine level behind the shrine structure... when it's clearly too big and would just exist right there in the overworld?

The asterisk* is there for a different reason: TOTK and BOTW are far too massive to load the entire game world (shrines or no shrines) into memory all at once. Instead, when you look into the distance, what you're looking at are LOD (Level of Detail) objects. They are less detailed versions of the real things, and they get seemlessly replaced with the more detailed versions as you get closer to them. But... Have you ever moved so fast in TOTK (say, by diving from the Sky into the Depths) that the game sort of freezes for a bit? That's because the game is busy loading the more detailed objects in the area you're approaching, and you're approaching way too fast. So the game doesn't know what else to do but pause you dead in your tracks so it can finish loading.

All this is to say that the game design principles of Switch Zelda's don't really work unless you load, and deload, large amounts of data from disk, or at best memory. A switch with a fast solid state drive and humongous amounts of RAM could make load times minimal, but as long as you need to load or deload anything, then that is a process that takes time.