I found this a couple days ago, can't get any videos of it but there are a couple videos (not much, hasn't been documented too well) floating around.

Basically, when you start to climb down anything (except ladders for some reason), some value is saved into memory (assuming its some value to tell the game where to attach link). This value isn't wiped from memory when you load another file, so when loading into a shrine there's a large displacement from where you load.

There are two main factors that influence this position where you spawn.

1. Where you are in the overworld (also works in shrines), scaled to around 1/5th. Testing has shown that the hyrule castle courtyard is approximately 0,0 on the overworld, so around there is where you need to climb down. You can also make ice blocks in certain shrines, but it wont displace you much.

2. There is an approximate 21.5 unit displacement based on the direction you're facing when you climb down.

Basically when theres a prompt to climb down, press A and open the inventory at the same time, then load a save file thats in a shrine, you'll spawn away from where you're supposed to. Doesn't work well at all on the overworld unfortunately.

This could be used with the shrine outside Hyrule castle, or maybe even the one inside the library to teleport inside the sanctum maybe? Would be interesting.

Did some more testing, it seems that shrine to overworld DOES displace your overworld spawn position, but it snaps back the next frame. If you do the trick while on the plateau, itll actually void you out as if you left the plateau early. I believe the shrine entry cutscene prevents this.