> why do we invent these formal languages except to be more semantically precise than natural language

To be... more precise?

On a more serious note, cannot recommend enough "Exactly: How Precision Engineers Created the Modern World" by Winchester. While the book talks mostly about the precision in mechanical engineering, it made me appreciate _precision_ itself to a greater degree.

Rhetorical sentence? My point is that back-translation into natural langauge is translating into a less precise form. How is that going to help? No number of additional abstraction layers are going to solve human confusion.