> Human language is imprecise and allows unclear and logically contradictory things,

Most languages do.

"x = true, x = false"

What does that mean? It's unclear. It looks contradictory.

Human language allows for clarification to be sought and adjustments made.

> besides not being checkable.

It's very checkable. I check claims and assertions people make all the time.

> That's literally why we have formal languages,

"Formal languages" are at some point specified and defined by human language.

Human language can be as precise, clear, and logical as a speaker intends. All the way to specifying "formal" systems.

> programming languages and things like COBOL failed: https://alexalejandre.com/languages/end-of-programming-langs...