English was not developed to facilitate exact and formal reasoning. In natural language ambiguity is a feature, in formal languages it is unwanted. Just look at maths. The reasons for all the symbols is not only brevity but also precision. (I dont think the symbolism of mathematics is something to strive for though, we can use sensible names in our languages, but the structure will need to be formal and specialised to the domain.)
I think there could be meaningful work done to render the statements of the results automatically into (a restricted subset of) English for ease of human verification that the results proven are actually the results one wanted. I know there has been work in this direction. This might be viable. But I think the actual language of expressing results and proofs would have to be specialised for precision. And there I think type theory has the upper hand.
Given the choice I'd rather use Python than COBOL even though COBOL is closer to English than Python.
I think it is more important to be close to English than to programming languages, because that is the critical part:
"As close to a programming language as necessary, as close to English as possible"
is the goal, in my opinion, without sacrificing constraints such as simplicity.