> Ask it to write tests that maximise code coverage
That is significantly harder to do than writing an implementation from tests, especially for codebases that previously didn't have any testing infrastructure.
Give a coding agent a codebase with no tests, and tell it to write some, it will - if you don’t tell it which framework to use, it will just pick one. No denying you’ll get much better results if an experienced developer provides it with some prompting on how to test than if you just let it decide for itself.
A lot of libraries document invariants that are either not checked at all, only at runtime, or somewhere in between. For instance, the requirement that a collection not be modified during interaction. Or that two region of memory do not overlap, or that a variable is not modified without owning a lock. These are all things that, in principle, can be formally verified.
No one claims that good type systems prevent buggy software. But, they do seem to improve programmer productivity.
For LLMs, there is an added benefit. If you can formally specify what you want, you can make that specification your entire program. Then have an LLM driven compiler produce a provably correct implementation. This is a novel programming paradigm that has never before been possible; although every "declarative" language is an attempt to approximate it.
The problem is there is always some chance a coding agent will get stuck and be unable to produce a conforming implementation in a reasonable amount of time. And then you are back in a similar place to what you were with those pre-LLM solutions - needing a human expert to work out how to make further progress.