These are good criticisms that I, as someone still playing through the game, haven't thought about. Having different themed shrines would have been great. The game definitely could use more variety.
The world is big, yes, but that adds to the wonder. Fun per inch, as you put it, is like saying white space is unimportant in UI design -- completely wrong. There's benefit in having some nothing in the world. As you're starting out, the game is a big world for you to discover. At the end, sure, maybe you're jaded. But the sense of continual discovery I'm experiencing now is wonderful. Again, agreed on variety.
I also generally hate open world games. Full of nothing. Zelda is different. It has meaningful discovery and exploration imo.