I see it as a common vocabulary to talk about tools. It's simpler to say "I made a singleton" than to describe it.
Just like we have words for a nail, a screw, a hammer. If you had to say "I used a tool that I find works well with nails", that would be annoying and ambiguous.
Now of course, if you quickly screwed something with your swiss-army knife and a junior came and told you that this is wrong, because you should always use a proper screwdriver, and therefore you should rent a car and drive 30min to go buy it right now, you would kindly tell them to fuck off. Doesn't mean that there is no value in the concept of a screwdriver itself.
You point out the cultural issue that this creates and sweep it under the rug, violently.
The thought model complicates the process of writing new code, "what pattern do i need here?" and the perception of existing code, "oh this is pattern X, why isn't that communicated clearly?". The truth is that design patterns are at best stagnant in quality and quantity over time (GoF is over 30 years old!), but the quantity and quality of problems is infinite.
I've thought in patterns quite some time in my early career. With my colleague back then everything was an pattern and we were kind of in sync with that approach. But it quickly falls apart if you have peers that are less try hard on it. You can spend days, weeks, months to study design patterns and then have to explain it to someone in 5 minutes that simply doesn't care. I can't blame anyone to not care, so that has to be accounted for.
I think the common language argument is tempting, but also too stressed. Good and useful programming knowledge is bound by reality. An integer is a indisputable thing that is always useful. A "singleton" is just a fancy rephrasing of "global state".