As for the building intuition, perhaps I am over-estimating what most people are capable of.
Working with and building systems using LLMs over the last few years has helped me build a pretty good intuition about what is breaking down when the model fails at a task. While having an ML background is useful in some very narrow cases (like: 'why does an LLM suck at ranking...'), I "think" a person can get a pretty good intuition purely based on observational outcomes.
I've been wrong before though. When we first started building LLM products, I thought, "Anyone can prompt, there is no barrier for this skill." That was not the case at all. Most people don't do well trying to quantify ambiguity, specificity, and logical contridiction when writing a process or set of instructions. I was REALLY surprised how I became a "go-to" person to "fix" prompt systems all based on linguistics and systematic process decomposition. Some of this was understaing how the auto-regressive attention system benefits from breaking the work down into steps, but really most of it was just "don't contradict yourself and be clear".
Working with them extensively also has helped me hone in on how the models get "better" with each release. Though most of my expertise is with OpenAI and Antrhopic model families.
I still think most engineers "should" be able to build intuition generally on what works well with LLMs and how to interact with them, but you are probably right. It will be just like most ML engineers where they see something work in a paper and then just paste it onto their model with no intuition about what systemically that structurally changes in the model dynamics.