It is simply that the Germans had broken every agreement that they had ever made
Well, no, they had acted in good faith with Italy, Hungary, Spain, Bulgaria, Turkey, Sweden and Finland by that point, and despite forcing Romania to return land, didn't betray any agreements with them. Now, that's not to say that Germany hadn't been an irredentist, untrustworthy aggressor towards the post-Versailles order or that Britain should have trusted them to keep their word this time, but saying that they were incapable of keeping their word at all is also disingenuous.
German cementing control over Eurasia would have made the next war an impossible war.
I don't think that would be the case. The only industrial power on the continent that was even competitive with Germany was France, and Germany would turn eastern Europe into agricultural colonies and central Europe into economic satellites, while a navy capable of actually clearing the channel and north sea would take long enough to build that Britain would have plenty of advance notice. Besides, this was far from the first 'impossible' war Britain faced; Napoleon
did cement control over Europe and still lost because human error is more powerful than numbers on spreadsheets, and unlike WW2, Britain gained a global hegemony from that.
Britain benefitted from the war simply because this was only way for it to survive as a free democracy.
Ignoring that describing Britain as a free democracy is farcical in any number of ways, Britain's internal political system would have continued to survive had it made peace with Germany; Germany was in no position to invade it by sea and the Battle of Britain demonstrated their inability to do so by air. However, their precious balance of power would be shot, which if fundamentally what British liberals cared more about.
Thats kinda the shitty thing about diplomacy and even basic business/relationships. The asshole/unreasonable client gets the better customer service.
Except Stalin wasn't being an asshole or unreasonable to the Americans a priori. In fact he was repeatedly shocked by how generous they were, especially compared to how they treated the British. This is almost entirely on Roosevelt and his and his administration's ideological sympathies.
Britain didn't want to accept it had been defeated in 1940, which is understandable. But rather than attempt to come to a negotiated settlement with Germany and save face (something Halifax proposed after the Fall of France), Churchill committed Britain to a war it was not prepared to fight or win on its own. There was no short or long term strategic or material gain for Britain from its participation in the second world war, unlike the first, and it effectively had to auction off its empire to the US for victory - which obviously raises the question of whether that could even be called a victory.
