I don't exactly disagree, but I don't think your analogies work.

Machines can lift more weight than humans, but we all encounter situations where strength is useful and machines aren't available or wouldn't be suited to the task.

Cars are faster and easier than walking, but they require roads and are not a possible substitute for all of the walking we do.

But "if LLMs can solve all coding problems perfectly", and assuming that's sufficiently true of cheap/free models, there will be no practical need to code by hand; it'll be something we do purely for the joy of it and/or as brain training (but a niche form of brain training, probably practically inferior to other forms that target skills we still need).