You are correct - fishing was pretty much a requirement for high level content.
Giving AST the same cards, but disabling all forms of being able to swap those cards would just make AST horribly weak.

Fishing sucked, but was required because of how weak the cards were besides Balance/Spear/Arrow. Even then, sometimes it was almost worth it to try and Arrow.

What you are suggesting isn't bad because it takes away fishing, it's bad because it takes away fishing + gives AST the worse card system. It's the worst of both worlds.