Very good points. Often I find that Web developers also expect the blind to navigate just with the tab key and enter keys. This is true in LinkedIn and some travel booking sites.
Also of note, is that web accessibility documentation have had deep discussions about what a link is versus what a button is, and they don't really seem to take into consideration the visual appearance of the item in question. Except for next/previous buttons on training sites, a button is usually considered to be an item that acts on other items in the page for example (remove, add, purchase) Sometimes Web developers will mark an item up as a link and then use a special attribute to tell the AT that it is a button. Think of those places where there was a click here button and you couldn't get it to work... this could be the reason.
One final point, not all screen readers use just first letter navigation within item lists. A search type capability could certainly be added to the panel invoked by NVDA-F7.