“Therefore it would have been worth a try not to betray the Poles.”
Failure to initiate WWIII against Russia with the Empire of Japan still intact and Germany in chaos doesn’t amount to betrayal. Using your logic, the United States betrayed not just Poland, but Czechoslovakia, Bulgaria, Romania, and all other nations living under Soviet oppression during the cold war. The U.S. weren’t even under obligation to liberate western Europe, much less all of Europe and Russia as well. You paint an unfair portrayal of America and her history by accusing her of betrayal.
The Poles were allies and friends from the very beginning who fought for the freedom of the UK and for the interests of the US like lions. A main reason why those Poles lost 20% of their population between 1939 - 1945 was the fact that they imposed the hardest resistance on nazi Germany you can think of. If this kind of resistance would have never happened, the D-day and the allied victory would not have been possible in 1944. The Poles, the Serbs and the Czechs weakend the nazi regime in a decisive way and Hitler had to wore out his forces in the oppression of those people. They sacrificed themselves for the US and the UK because they believed into being rescued and into the alliance that was declared by the UK on the 6th April of 1939 in the case of a war.
The occupation of Poland and Czechoslovakia was quite expensive for the occupiers and after the subtraction of the costs there was absolutely no benefit but a high toll on blood and material. Furthermore those Polish, Slovak, Serbian and Czech freedom fighters bond lots of German troops that could have been used on the western front against America and its allies.
The Poles would not have fought against the German millitary machine that much if they would have known that they are huckstered to "Uncle Joe", who erasured their intelligentsia in Katyn. Stalin and Hitler were on a par. Since America and the UK always concillated the conception of being members of the "western civilized family" to the Poles and declared alliances with them, it was indeed a shame- and reckless betrayal to leave them with a shrug of the shoulders in Stalin's little shop of horrors.
Shame on your leaders for doing that. I have lots of sympathy for Churchill and Roosevelt, but Yalta was the most fundamental mistake in their lives.
P.S.
Same could be said about other eastern Europeans, but the Poles were those who were declared allies of the Brits.