Doing programming in plain English would be just as cumbersome as doing math in plain English.
I don't think anyone can quite fully imagine the nightmare of trying to program in a recursively enumerable language[1].
In Utupia (aka Nowhere) we will have programs that a human being can know is correct. This might involve mathematical proofs, tests and whatever. But how do we know that those things are correct?
In some cases, it would help if we had an English text explaining what the program should doo + computer verification that the program really does that. The English text is only one part of the picture -- but an important part.
This is what acceptance testing tools like Cucumber and Robot try to do; but they avoid actually parsing English. Computers are getting better at parsing human languages, so I expect improvement in this field.
Modern models learn to achieve goals in increasingly sophisticated 3d environments and even learn execute commands in some very limited form of natural language. You could say that the question of achieving more humanlike performance may be "just" a question of engineering and scale.