One request from me would be for them to bring back the + operator and favour it instead of quotes, since Google Plus integration doesn't seem to be a thing anymore.
Honestly I think using quotes for that is probably better, even though + was a bit less typing. You wouldn't believe how many people search for [tar -xvf] and are confused as to why none of their search results contain the string xvf. It's hard to come up with operators that are easy to type and will never collide with their normal meaning in language, and I think quotation marks work much better for that than + did.
I explained elsewhere that it's very unlikely to come back because we actually do try to match + in queries now for thing like international phone numbers, and also as someone else noted, there's any number of names that make use of it (Disney+ for example).
How about a heuristic of: If the user phrases their search as a natural language query ("what is...?", "how do I...", etc...) then use whatever weird relevancy metrics and search word substitution your research suggests will answer the question best. OTOH, if the user appears to phrase their search as just a list of keywords, search for all the words verbatim.
They already do query classification for things like Google Calculator. Extending the classifier to switch between "natural language query" and "strict keyword search" seems like a reasonable extension of that idea.
Ok - I totally understand the intent, but NOOOOOOOO!!!! (or more clearly: I have no problem with them trying this, but it doesn't solve my use case)
The entire reason I ask is because I don't want google to try to interpret my search query and change it - I don't want it to guess what I'm looking for using [insert classifier of choice] - I want it to do as close to a text scan for the exact search query as I can get.
Inconsistent tools are much harder to use. I really don't want to have to play a cat and mouse game with my search tool, and I don't want to have to have memorized all the "games" google is playing with my query and understand how to turn them off.
Please let me turn on verbatim mode and leave it enabled. Ideally across my google account, but I'd settle for just that device/application.