I tried to find a counterexample and I couldn't! I believe you that quotes really are working. What's confusing though is that a quoted word or phrase often doesn't show up in the Google results snippets. This is certainly the reason why people think quotes aren't being respected.
Though, why does enabling "Verbatim" (in tools) on a search reduce the number of search results if all my terms are already quoted? Enabling Verbatim often does it make it feels like my queries are interpreted more literally, but if quotes are already being respected I don't understand how Verbatim would reduce the number of search results.
I agree, it would be easier if it were in the snippet. That's something we're looking at. I believe it used to, but sometimes the quoted part might not have been the best overall snippet to use. But as said, we might revisit that.
On the counts -- basically, it's all really rough estimates. We make a rough quick count, you go deeper into the page, we make a fresh estimate. It can change, and it doesn't always make sense and personally, I'd hope we just get rid of counts because of this, perhaps more confusing than helpful.
Though, why does enabling "Verbatim" (in tools) on a search reduce the number of search results if all my terms are already quoted? Enabling Verbatim often does it make it feels like my queries are interpreted more literally, but if quotes are already being respected I don't understand how Verbatim would reduce the number of search results.