There are multiple factors involved, but briefly ... as though I can be brief ...
In '64 or '68 (Goldwater on principal, Nixon because he was Nixon), the GOP started doing things that attracted the folks who had been offended by the Civil Rights legislation of the Johnson years. They started with a wink and a nod, but became ever more obvious. It's my fault that I was in denial about this until around 2010, but there you have it. It was still there and growing.
They added all of the culture "stuff" along the way. It fit with the underlying message about keeping the right demographic in charge. A modern version of "Gone with the Wind" developed. A fable about a time that never was.
Along came a fellow with the skills of an old time vaudevillian, he could read the room, and the ethics / morals of ... what? Doesn't matter. He became the leader of the MAGA band, a group who believed that he would take them back to that time that never was.
All this was enabled by Watergate.
Post Watergate, there were a lot of reforms. One of them was to eliminate the "smoke filled rooms" full of professionals and replace them with the will of the people as demonstrated in primary elections.
It is through the primary election process that the MAGAs can impose their views on the GOP. And the so-called leaders of what was once a great political party have avoided confronting the problem since 2016, by which time, it was really too late. Insert here the Churchill quote you used in your post. It fits exactly the GOP response to the rise of MAGA power, a rise that began in earnest around the turn of the Century. But the first crisis came when those leaders had at least three clear shots at confronting the problem: impeachment 1, impeachment 2, and election denialism.
Finally, when those opportunities were wasted, the fate of the GOP probably sealed. Not this year, not next, but before the decade is out, it will probably have turned into a minority party akin to the Libertarians. Hopefully a new party, Forward?, will rise to take its place in the center-right of our nation's political spectrum.
In closing, I do not mistake Cheney for Churchill, save for their shared experience of being cast out for their commitment to telling the truth as they saw it. And, while she ain't Churchill, a lot of the folks in the GOP have to stand on tiptoe to see eye to eye with people like Chamberlin and Quisling.
I weep.