So I finally beat all shrines in the game, located all memories, and beat Ganon.
Based on what I learned from the memories and also reading the diaries in Hyrule Castle, Zelda kind of really is to blame for things going FUBAR when the Calamity returned.
Conclusion first: She should have given the Sheikah Slate to Link when they first got it working.
Reasoning: we know from the memories and diaries that Zelda was fully aware Link was the "chosen one" because he was chosen by the Master Sword. All of the Champions knew this too, Revali makes reference to it in his Divine Beast flashback, Zelda mentions it numerous times, etc.
There's also a memory in which Zelda is trying to use the Sheikah Slate to open up a shrine. She's figured out how it's supposed to work and even mumbles to herself that it should work if the chosen hero were to try it. But then Link shows up and Zelda goes all tsundere and yells at him for following her around and being baka.
Later on the Calamity returns and everyone dies, Link falls in battle, and Zelda confines herself to Hyrule Castle to try and contain Ganon.
Link and Zelda spent a fair amount of time traveling Hyrule together. It's not exactly clear how much, but at least months and possibly a few years.
Link could have been using that time to visit the shrines and increase his power. Simple as that. 100 years ago Link was a total badass but only had 3 HEART CONTAINERS. If Zelda had not been such a tsundere control freak and just gave Link the slate he would have been a powerhouse by the time the Calamity struck.