My impression is that USENET died because it lacked reasonable spam prevention measures?

Spam started on Usenet. The Canter & Siegel visa spam! The anatomically correct chocolate heart! Ah, memories.

So yes, a lot of it was overrun by spam for a while, but countermeasures were developed, and eventually the spam was brought down to the level we see today. My impression is that Usenet faded because blogging and web forums were invented, and most people voted with their feet. And then public access to the Internet exploded, the general public never even knew there was such a thing, and USENET faded into an obscure backwater of old-timers, which has probably contributed to it lingering on for as long as it has, under the benign neglect of Google and whatever sysadmins still run nntp servers. I've just looked into rec.arts.sf.fandom and it's still going, but I recognise nearly all of the posters' names, which implies that it's the same people as it was years ago, perhaps thinned by age. I've nothing against them, but I'm not going back.

Is USENET still USENET, even? That is, are there still nntp servers propagating the messages to "thousands of machines throughout the entire civilized world"? Or does everyone go to Google Groups to use it?

USENET developed as it did because of the technological and social environment of the time, and faded when that environment changed. No-one would invent it today, except in the form of a heavily decentralised and encrypted medium for secret discussion.