Big brands spend millions establishing a particular look, style, format. They don't want you to treat their sites as merely a set of APIs to scrape and customize based on your own style preferences. They want you to have a branded experience.
It doesn't really matter what they want. Chat interfaces are doing this from the opposite direction, pulling the data down and explaining it to you, it's not a big leap for LLMs to turn their markdown responses into a slightly richer experience you can browse natively.
The point of the OP is that the companies would willing cooperate and replace their websites with LLM consumable APIs.
It's a different question whether this will happen despite their objections, as a kind of logical conclusion of the greasemonkey plugin.