There is no way the Allies would allow the adoption of the black-white-red flag which was associated with monarchists and the far right under the Weimar Republic. Indeed, it was never seriously considered: "While there were other suggestions for the new flag for West Germany,
[52] the final choice was between two designs, both using black-red-gold. The
Social Democrats proposed the re-introduction of the old Weimar flag, while the conservative parties such as the
CDU/
CSU and the
German Party proposed a suggestion by Josef Wirmer, a member of the
Parlamentarischer Rat (parliamentary council) and future advisor of chancellor
Konrad Adenauer. Wirmer suggested a variant of the 1944 "Resistance" flag (using the black-red-gold scheme in a
Nordic Cross pattern) designed by his brother and
20 July co-conspirator Josef.
[53] The tricolour was ultimately selected, largely to illustrate the continuity between the Weimar Republic and this new German state. With the enactment of the
(West) German constitution on 23 May 1949, the black-red-gold tricolour was readopted as the flag for the Federal Republic of Germany.'
https://en.wikipedia.org/wiki/Flag_of_Germany
The Allies had fought two wars with Germany, not just one (and of course in the case of France there was the Franco-Prussian War as well) and while they were willing to recognize that the Kaiserreich had been less evil than Hitler's Reich, they sure as heck did not regard it as a good thing--or as superior to the republican traditions (dating back to Frankfurt 1848, not just the Weimar Republic) embodied in the black-red-gold flag. And indeed to some extent the black-white-red flag bore the stigma of the Nazis as well as of the Kaiserreich, since from 1933-35 the Nazis had reintroduced it as a German national flag (coexisting with the Nazi party flag).
I would note that adoption of the black-white-red-flag would be a priceless propaganda gift to the GDR which could claim it was the only true inheritor of German republicanism, and that the West was dominated by the far right, as shown by its flag. But that's academic, because such adoption was not going to take place