To put it somewhat in context, the two types of scrapers currently are traditional http client based or headless browser based. The headless browsers being for more advanced sites, SPAs where there isn't any server side rendering.
However headless browser scraping is in the order of 10-100x more time consuming and resource intensive, even with careful blocking of unneeded resources (images, css). Wherever possible you want to avoid headless scraping. LLMs are going to be even slower than that.
Fortunately most sites that were client side rendering only are moving back towards have a server renderer, and they often even have a JSON blob of template context in the html for hydration. Makes your job much easier!