In terms of labeling emails that need replies for me if it's still in the inbox if it needs a reply / action. If I'm done with an email I archive it.
In other words, to be the most useful, a label needs to have as few uses as possible, or else become a separate folder for perusing. And if a label looks just like a search, skip the clutter and just do the search. If its a bin for perusing, well, good on this new feature.
I can't imagine when I'd want to view all emails labeled "Invoice", for instance. If I know I'm looking for a software key, then doing a search will be much faster than clicking on the label and eyeballing it for the right one.
In your example that's also something you have to label manually. If you forget one and then look through the "Invoice" label folder and don't find it, you have to go do a search anyway. As much as possible I want to reduce the number of things that could be screwed up by mere forgetfulness. So by not using labels there is no chance of screwing it up, and there's less work to do to boot.
So I'd rather not concern myself with taking the time to organize my to-be-archived emails into labels unless it represents a non-trivial gain, and I don't think the gains are very large in nearly every practical case. "Needs-reply" is the only one, since it represents a separate queue of to-do emails.
I think your logic is seriously flawed, but as long as it's your email and not mine, so be it!
Labelling is a way of demonstrating intent, though. I want to see tax-related invoices for the organisation I'm helping out with; not everything actually has the words "invoice" in it, or mention the organisation.
Either you need to introduce AI for me to teach, or let me impose search information on the email itself. Tagging is just a way of doing the latter.
Every time I read comments on HN about how people have these "amazing" systems of filtering and labeling in gmail I always wonder if there's anyone else who uses gmail like I use it.... turns out there is and they've doubled my high score.