Building a house rests on a long history of crafting and engineering. If working builders needed to understand abstract algebra we might have a lot fewer of them. The foundation of construction isn’t really mathematical. You can build a house without even doing a single measurement. Accessibility for beginner builders is in fact very important.

I’ve used Agda. It’s extremely difficult. Even pretty basic proofs can be extremely tricky; just figuring out how to use the transitive equality proof syntax is a challenge. You quickly run into the need for stuff like “universe polymorphism” which comes with a huge and terrifying theory. If this is the only way to make decent programs then we’re doomed!