LLM output can't really be trusted so I need to "proof read" it and convince myself that it is correct. In the language I use every day and have a high degree of fluency, it's faster for me to simply write what's in my head than to proof read unknown code. So how can LLMs make me more productive in actual programming?

I use an LLM to generate ideas, to rubber duck, to get a lead on unknowns, and to generate boilerplate occasionally. So I do everything except replace the coding part because that's what requires the most precision, and LLMs are bad at precision. And yet, people claim massive productivity gains in specifically coding. What am I missing?