Note: Answers that go "just write a query like `field1 ~ name and field2 ~ name and field3 ~ name and etc.` are not helpful.
I want to be able to quickly and at any time with no preparation search all our tickets for mentions of specific product names in *any* and *all* fields, whether it's text, keywords, summary, component, or ANY field.
text is uselessly broken for it, as it for example fails if one of the search word is in one of the fields, and one of the search words is in another field. In that case searching eg `text ~ "word1 word"` fails to find the issue.
Also, did you actually click "accept answer" on your own answer?
Yep, I'm just confirming that you can't really do it. The problem is with the way custom fields, indexing and stemming is implemented, building a "search everything" actually becomes complex and potentially a massive resource hog. So Atlassian have dodged it by not doing it. The text search is deliberately fuzzy, as a lot of humans don't work with exact search in text, and that's part of what makes search everything harder.
If I did click on accept answer, then it was a mis-click. If you saw something about it, then I probably did do it, it wouldn't be the first time I've hit it accidentally. When I do, I try to remove it straight away, as it shouldn't be up to me. I suspect I've done that here, but I don't remember where my last few mis-hits were. (FWIW It's not even useful for "gaming" the points system - no-one gets any points for marking their own stuff right!)