Any searches that aren't looking for an immediate answer. When I'm searching, I don't want the search engine to find an answer for me. I want the search engine to provide me with a list of websites that touch on the topic I'm looking for, so I can get a "big picture" of what's out there, review them, and put together the information I'm looking for from the mosaic that I have been presented.
I don't want the search engine narrow my view to a tiny selection of websites or, worse, try to summarize the contents of the websites. That's not useful to me in terms of what I use search engines for.
Stateful search is really only useful for narrowing things down. That's not what I want the machine to do except in terms of paying attention to the keywords I want (and the keywords I actively don't want).
I totally understand there are use cases where what I actively don't want may be exactly what is desired. That's just not my use case. That's why I'm not saying there shouldn't be such search engines. I'm just saying that I hope my use case will also be possible, or web searching loses a whole lot of usefulness to me.
I would expect stateliness/statefulness to work in both directions. Instruct it to broaden its interpretation.
If you provide stateful search with keywords it will return the list you want. Then just dont follow up. Im probably ok with a couple extra instruction words when looking for traditional looking search results. "list sites re [keywords]"
It'll be interesting to see how the product changes over time when it retains some state about your preferences. Maybe you can teach it a bang abbreviation to always give you the type of result you are looking for. (!lw)
(You already see limited state on google when you search something, then search something unrelated and some results for the former keywords show up highlighted. Google sometimes thinks a new search is a folloup search to the previous one.)
But it would be a loss for people doing research.