Learn English – The usage of “let alone”

Both your example sentences are perfectly fine and exactly how people use the expression.

The Urban Dictionary definition is badly worded (if you’re just getting started with using Urban Dictionary, get used to this—most entries on there are horribly worded). What it means is that you can also say something like,

“Do matrix operations? Gah, I’d rather bleed from the eyes!”

This emphasises that even bleeding from the eyes is more appealing than doing matrix operations.

Note:

After a set of exchanges in the questioner's meta question concerning issues connected with this one, I have edited parts of my response in order to soften its tone.

The OP later substantially changed the question from its original form in the light of this response and the comments under the question; this should be taken into account when reading the points below, which all relate to that original version of the question.

I have not attempted to respond to the most recent version, as I think there is no reliable way to assess or quantify the trends that the questioner is now asking about.

Partly for this reason, and partly because the question now seems to me to be excessively broad in the scope of usages it is asking about, I think there is a good case for deleting this question altogether, and for the questioner to replace it with a new one that is more narrowly focused.

It seems to me that your question makes some unjustified assumptions.

You focus on the supposed decline of "Thank you" as if there were no other ways of expressing gratitude; nor do you adequately support your premise that the expression of gratitude is declining. At a minimum, the absence of convincing evidence, notwithstanding the sources you cited, invites challenge.

For instance, the Food Network UK poll returned distinctly mixed findings, and the Daily Mail article describing it fails to include the details of the questions and other methodological aspects of the poll that would allow its readers to make an informed judgement about the poll's reliability.

The NPR article you mentioned is essentially a mashup of contradictory opinions, though one of the people quoted in it did have this point to make which rather undercuts your own position:

However, when it comes to the actual articulation [of formulas that mark civility], she [Cindy Post Senning, a director of the Emily Post Institute in Burlington, Vt.] says, "the words we use do change."

For example, Senning says, it is important to show respect for other people by greeting them when you first see them — in the hallway, at a meeting, on the street. The form of greeting, though, has morphed over time.

"How do you do?" became "Hello, how are you?" which eventually changed into "Hello, how are things?" Or "How's it going?"

As a result of the metamorphosis, Senning says, "today it would sound a little stilted and perhaps even disrespectful if a sarcastic tone is used to say 'How do you do?' "

And in the transcript of the Today segment you mentioned, we read the following snippet:

Ms. TWERDAHL: We're all perceived to be very, very busy and people's perception is that it takes more time to be polite than it does to just rush through something and be impolite.

But a couple of paragraphs later, this contention is contradicted by the empirical observations of one of the show's reporters:

ALMAGUER: Are we really too busy, too important or just too inconsiderate to say please and thank you? To find out, we headed to this Los Angeles coffee shop. After two hours and 27 customers, not a single person, not one, failed to say thank you. A few said please, but they were all thankful.

The rest of the discussion largely consists of all the participants platitudinously agreeing on the importance of civility as a social lubricant, plus some anecdotal assertions that parents today are too lax in enforcing the habits of civility on their children.