I'll start off by saying this: For the most part, I don't like shrines.
Now, I'll clarify that further. There are shrines that I genuinely liked. These would be the ones that contain several puzzles at once, or one puzzle with multiple steps. Blue Flame springs to mind, but I know there were a few others whose names I don't recall that were about as good. But I found myself getting very irritated with the very simple, easy, single puzzle shrines because they rarely took more than 2 seconds worth of thought to solve. If I'm gonna sit through several minutes of loading to get in and out, there might as well be something of substance to wait for. Otherwise you're just adding time to my game that I don't need. They also didn't feel fulfilling being so short or easy, even though a few of them were actually somewhat clever. They get your mind working a bit but then they're just over. Often times I would find myself wishing they had a few more rooms that built on from the mechanic they'd established.
When I get down to it, I don't think I want shrines to reappear like this. Many of them felt like filler, and even though some of them came at the end of a shrine quest, I always got irritated when they were just the "walk in and collect your price" types. You might argue that "well completing the shrine quest was the puzzle". Maybe. But my reward for completing it should have been an excuse for some more really cool gameplay. Not a bull**** "gimme".
I understand what the point of the shrines was: they didn't want to strongly interrupt the flow of the "explore this whole giant world" gameplay that they put so much time into crafting. But I think the game suffered because of it. I mean, this may seem a tad silly but I've always thought of Zelda games from a lens of three gameplay elements that sorta mirror the parts of the Triforce: Fighting Monsters (Power), Solving Puzzles (Wisdom), and Exploring Dungeons (Courage). And for the most part, the best titles in the series have been the ones where these three pieces were more or less in harmony with each other. So it's my hope that for the next game, they ditch this mentality of chopping up proper dungeons into lots of tiny rooms and sprinkling them across the overworld. What I hope they do is return to having legit dungeons, and then also having some completely optional dungeons thrown in there. One idea I had a while ago was to base the dungeons around an idea almost like a compass rose. Not in literal terms, like direction, but more like how we have North, South, East, and West, but also directions inbetween those like Northeast or Southwest. You can have your standard elemental dungeons, then 4 more for what I'll call 'primal force' dungeons. Earth, Air, Fire, Water, Life, Death, Order, Chaos. Have the elemental ones be the required ones, then top it off with your Ganon's Castle or whathaveyou, then just have the other four all be based around their aspects. The Life dungeon can be somewhere teeming with life, and you do stuff like grow magical stalks to reach new areas or use magic to make stuff grow and change to work your way through. Death could be your excuse to go all out with the Poes and ReDeads and marinate in that delicious 'Bottom of the Well' type jazz. The Order dungeon can be something like the usual "ancient Shiekah trial" thing where it's obviously artificial and stocked with lots of puzzles that reward logical thinking (like your laser light and sliding block puzzles, or monsters that require observation to defeat instead of brute force), and lastly your Chaos dungeon can be something that is mostly about straight swordplay. Possibly some sort of massive Bokoblin camp in a rundown coliseum or something. If you really want to, you can make the optional ones be a little less complex than the main ones, but they should still be proper dungeons.
Anyway, that was a bit of a tangent but I just used it to illustrate that there are better options. What I'd like to see from something like what I mentioned above is a way to organically weave the existence of these places into the feel of the world, put them in places that make sense, don't lead the player by the nose to get to them, drop your hints or do whatever to make even finding these places feel like a great reward, filled with mystique and the sense of adventure. I mean, does anyone remember what it felt like the first time they played an old Zelda game? I mean, the original LoZ wasn't even my first one, it was like my 5th or something. I still remember the thrill I got when I stumbled upon the first dungeon. The way this old tree just sat there with a yawing, cavernous mouth... something felt strange and wonderful to find it like that. I mean, just think how anticlimactic some of the shrines are. You make an arduous ascent up some mountain, when suddenly you hear the music fade in. Before you is a glowing Shrine, the wind blows softly, a bird takes wing... something about this place feels magical. You open the door, descend to the chamber below.... only to pick up a box, set it on a button, and leave. I mean, come on, the **** was that all about?