I don't think there's ever going to be a truly historical answer to this, so let's consider it in a hypothetical fashion.
The piano is a great and easily recognizable accessory to have available as a backdrop for meaningful conversations between characters in a film. They can sit at or near it, perhaps picking away wistfully at the keys, with all of the melancholy promise that an instrument in desolation can offer. It's very similar in this fashion to the "beat-up gramophone" that also appears so frequently in such films, no doubt playing the languid notes of Ms. Edith Piaf. The mood of nostalgia seems to be inescapable in the western WWII film (as compared to the hideous realism of something like Elem Klimov's Idi i smotri (1985)), and this sort of omnipresent musical accompaniment helps it along nicely.
Within the narrative world of such films, I can imagine a number of practical reasons why the piano would noticeably appear in streets with such regularity.
Pianos are large and sturdy enough that they can still effectively "work" even after having taken some punishment -- though not a lot.
Their size also means that they really can be visible in a way that a hastily discarded violin or harmonica or something can't be. Who knows how many abandoned violins we've seen in the background of shots in such films without really noticing them? And what untutored GI could pick up an abandoned violin (which also needs a bow) in the same way that he could pluck idly at an ivory key?
That pianos should be in the street at all during such times is jointly a function of their commercial value and their physical size. They're just expensive enough for a fleeing family to want to save them, if possible, but also so burdensome that they'd be among the first things abandoned during the act of headlong flight. The value that would see them dragged towards the door or out into the street in the first place might also see them become popular targets for looters, both civilian and military alike. These looters still wouldn't be able to get them very far from where they were found, unhappily.
These, at least, would seem to be reasonable explanations for the phenomenon you've noted.