Every "mobile friendly" menu site is able to show maybe 5 items on the page at once
This is due to accessibility regulations. Apple design guidelines and Material guidelines explicitly state how small font can and should be. Ask any designer you know.
My phone has a text size setting, and if I needed bigger text for readability I could set it - why can't we have that conveyed as a user preference somehow?
You just said it yourself. Your phone provides that preference. But a good default is essential, and given to us based on Apple and Googles research, which was probably actually done by Nielsen Norman Group
The "good default" should be the default size that the browser uses, in my opinion. The designer of the website is not in a position to know what the best font size is.
