"Late stage" or "late capitalism" always suggests to me that the user has inside information on the sell-by date. I don't disagree about the proportion of attention.
I suspect it's a combination of looking around and going "this can't possibly be stable" combined with a degree of wish-fulfillment.
It has more to do with the idea that the system has evolved and advanced for a while. It's not so much about the system ending soon, as it is about it being deeply entrenched and widely adopted, its long-term negative consequences having had time to manifest, and/or being the late stages of a deliberate long-term agenda.
That might be reading into it too much. I'm pretty sure it's just a joke that capitalism is cancer. As in, "late-stage cancer".
It's funny that the phrase was coined in 1902 and fell out of fashion by about 1970 and was revived in the 2010s. I guess what's old is new again.
It's people who believe Marx's thing about how "boom-bust" cycles will eventually destroy capitalism. Unfortunately, Historical Materialism is utter and complete bullshit.