Also Franz of Bavaria is Catholic, and thus marrying him would have caused Elizabeth to forfeit her claim to the throne under the then-active laws of succession. I don't think that anyone would have been prepared to change them at that point just so Elizabeth could marry a landless German (especially less than a decade after WWII).
Hell, Philip was a landless Greek and there was concern in the capital because of his sisters that were married to landless Germans (some of whom were Elizabeth's own cousins - the grand duke of Hesse-Darmstadt and Baden, the duke of Brunswick-Hannover, the prince of Hohenlohe)) who were Protestant.