I'll take a slightly different tack on the second part of your question…
Did [the idea of setting up a Jewish state in defeated Nazi Germany] gain any traction? Why / Why not?
One of the reasons why this idea could not have gained much traction is because Palestine had already become a major center of Jewish population, society, and power by the time the Nazis came to power in Germany.
There was significant demographic momentum and political will to establish a Jewish state in Palestine before World War II and the Holocaust, and these only increased with the flood of survivors who wanted to get the hell out of Europe during and immediately after the war.
Per demographer Sergio DellaPergola (screenshotted from this Wikipedia article), the Jewish population of Palestine had reached about 175,000 in 1931, before the Nazi takeover:
At the end of WW2, Tel Aviv (founded 1909) had an overwhelmingly Jewish population of about 200,000, the ancient port city of Haifa was almost 50% Jewish, and Mandate Palestine was dotted with kibbutzim and moshavim — many of them founded during a wave in the 1920s, but some older.
Basically all of the prominent political and military leaders of post-independence Israel had roots in Palestine extending well before WW2:
David Ben-Gurion immigrated to Ottoman Palestine in 1906, Levi Eshkol immigrated in 1914, Moshe Dayan was born on a kibbutz in 1915, BenZion Netanyahu — father of Bibi — immigrated in 1920, Yitzhak Rabin was born in Jerusalem in 1922, Ariel Sharon was born on a moshav in 1928, Shimon Peres immigrated in 1934… and President Yitzhak Navon's ancestors had lived in Jerusalem for 2-300 hundred years before he was born there in 1921. I point all of these out as evidence that there was a well-established power structure and political establishment of Jews in Palestine before WW2. If there hadn't been, we would expect to see a lot more wartime and post-war immigrants to Israel among its early leaders… but we simply don't.
Obviously, no one was talking about establishing a Jewish state in Germany as Jews were being murdered en masse by Nazis. It's hard to figure out exactly how many Jewish refugees immigrated to Palestine during the war, but 100-200,000 seems like a good guess. The British Mandate severely restricted Jewish immigration starting in 1939, leading to armed rebellion by Jews in Palestine and organized, clandestine networks to bring Jews there.
Following the liberation of the Nazi death camps (1944-1945) and V-E Day (May 1945) still nobody was thiking about establishing a Jewish state in Germany. The western allies, to a large extent, were consumed with finishing off the war in the Pacific, and confronting Soviet expansion. Many survivors of the Holocaust returned to their homes in Eastern Europe, but were soon confronted with renewed violence at the hands of their erstwhile neighbors; this was particularly severe in Poland, culminating in the 1946 Kielce pogrom in which over 40 Jews were killed. After these events, Jewish survivors felt unsafe throughout Europe, and immigration to Palestine accelerated, aided by the clandestine Bricha movement which brought around 250,000 Holocaust survivors to Palestine in 1946-48.
So, to summarize, no one with a significant stake in the outcome or political clout considered setting up a Jewish state in defeated Nazi Germany because…
- Jewish immigration to Palestine was moving at a steady clip before the Nazis came to power, as was the political movement to found a Jewish state there (the Balfour Declaration had been signed in 1917).
- Hundreds of thousands of European Jews fled the Nazi regime and the Holocaust between 1933 and 1945. Few countries would accept them, especially once the war began, and Palestine was a logical place to attempt to flee to.
- After the defeat of Nazi Germany, renewed antisemitic violence in Europe convinced hundreds of thousands of surviving Jews to flee. Zionist settlers in Palestine had become organized and strong enough to defy the British Mandate authorities and bring hundreds of thousands of Jews there.
- During the Nazi era (1933-1945), the Jewish population of Palestine increased by several hundred thousand through immigration, while the Jewish population of Germany decreased by almost half a million through emigration and mass murder. The "momentum" for founding a Jewish state was towards Palestine, and away from Germany, in every possible respect.