“This was a nice evening” is also difficult to characterize as not caring about which evening it is. As are books titled “An Introduction to XYZ”, where both the authors and the readers will probably care about the specific book.
I'm going to a bank, a shop, a dentist - I've found a new one and I may well be about to describe it to you.
"A nice evening" - there have been ones before, there hopefully will be again, this was one of them.
Here it only sounds OK if you make the adjective stronger ("this was the nicest evening", though you'd probably avoid "nice" in this case and go with "best", "most amazing"...), or drop the adjective altogether ("this was the evening").
So nuance is that you might have many nice evenings, with this being one of — but what if you do not, and all are actually terrible except for this one? I guess with proper pronounciation of "THE nice", it can still work (we already talked about nice evenings and not-nice ones, so it'd be "this was the nice one"), but it'd be pretty awkward.
Edit: Here's a frustrating HN thread where someone tried to claim it makes sense, but it turned out his argument hinged on "well obviously all native English speakers regularly go to some store, right?" Screw the homebound.
I think the usage falls into this group: "The first group consists of nouns which refer to shared knowledge of the situation or context...",
When you're talking to people you live with it is true that they know which store you are going to. Friends and neighbours would have also have known up to fairly recently, when people still mostly walked for groceries and such to the few small stores nearby and made friends with people who lived close.
So, I'd say it's a bit of a colloquial hold over from walking times and construction taking a listener into confidence.
But again, people use this even when I have no reason to know which store they went to.
I’m not necessarily saying they should stop doing this, but it’s clearly not the usual kind of definiteness implied but the use of “the”.
A prescriptivist pedant might insist that this is incorrect, and they should instead say "I need to go to a store", but in my judgment as a native speaker, the version with "the" is more idiomatic, and the version with "a" sounds stilted.
So I feel the rule isn't always taken literally, but the vs a is selected based on whether something is up for consideration/substitution rather than something that's well defined and specified.
"Our house has a pool" for example. There is a very specific pool being referred to, but it's sufficiently indirect that "the" would never be used here without radically changing sentence meaning.
It's like saying "our house has a roof" — very similar, but nobody really cares about the roof, the focus remains on the house.
And he may be saying "a" about the word "nice" instead of about the word "evening".
Note: This is just my opinion and an attempt at trying to make sense of it. Purely subjective take as I usually refrain from making purely opinion based arguments.
All of the above is in my opinion, but I never state that and assume a good faith reader will take it as such (here for demonstration purposes only :)).
So in short, thanks for your opinion, and I agree this is the largely the basis for choosing between an indefinite and definite article, also opening them up to inquiry ("I am going to the store" — "oh, which one?"; compare to "I am going to a store" — "what are you getting?").
For instance, "the bald eagle is native to North America".
There is also "The" in names; The Beatles, The Great Lakes, The Bahamas, The Bronx, ...
The role of "the" depends on context: how was the subject treated in previous sentences in the conversation.
"I see a bald eagle out of the window. The bald eagle is huge!"
In this second sentence, there is no way that "the bald eagle" could refer to the class of bald eagles, because the previous sentence introduces the topic of the sighting of a bald eagle. It refers to that one.
If "the bald eagle is huge" appears out of the blue, not preceded by any discussion of any eagle, that tends to bring in the class interpretation.
I learned the above through Japeanese. A similar thing happens with the は (wa) topic particle; I realized that "the" works in a similar way in that regard.
"I play the piano"
And then there are those cases where you actually use neither!