To call something historically impossible is bad phrasing, because the most we can really say is that it is historically implausible. The Pharaohs daughter could have been eccentric, or perhaps just had pity, in short we don’t know.
However, beyond this, there are two points I would make concerning the idea of Moses being adopted. First, the capacity of his adoption, using the Bible as a source, and secondly the potential of Moses being a mythical figure.
In what capacity Moses was adopted is never explained in biblical narrative. We know that he was found and named by Pharaohs’ daughter, and that a Hebrew (Moses blood mother) was called to nurse Moses. Finally he became the daughter’s son. All this can seen in the Bible narrative^1 . However the idea of princedom is assumed because he is adopted as a son, but it is extremely unlikely that he would have been a prince. Not only because of the Egyptian obsession with blood purity (Pharaohs marrying their sisters and such), but because of when Moses is mockingly asked^2 who made him a prince. It is more likely that he was simply an adopted member of court or the household, rather than a true prince.
It is an area of debate as to whether Moses was a historical figure in the first place; with some arguing that he was not (I personally disagree with this). William Dever, in “What Did the Biblical Writers Know and When Did They Know It” (page 99), speaks of how he doesn’t believe there is archeological evidence, or even a gap in the evidence, large enough to support the Exodus in a biblical way, and argues that Moses was either mythical, or a myth grown around a man. One of his more famous quotes from “The Biblical Archeologist” (page 33) is that “'the overwhelming scholarly consensus today is that Moses is a mythical figure”. So, to answer your question from this light, Moses may not have been a historical figure to begin with.
In short, if you believe in the biblical narrative, Moses’ adoption is still a plausible possibility, simply because we don’t know how he was adopted, and if you don’t believe in the biblical narrative, some historians believe that Moses was not a historical figure, thus rendering the question moot.
*Edit:Formatting
It was a well known literary motif, especially in the Ancient Near East. The closest parallel is in the story of Sargon I (ca. 2334-2279 BC), the founder of the Mesopotamian Akkadian Empire, whose birth/origin story was still being retold in the Neo-Assyrian Empire during the reign of Ashurbanipal (ca. 668–627 BC). The narrative describes Sargon, the illegitimate son of a priestess, being placed in a basket made of reeds on a river. The story of Moses may have had a similar, but distinct origin, or it could have been influenced by the Sargon narrative, which was known throughout the Neo-Assyrian Empire and was arguably contemporaneous with the canonisation of the Old Testament.
There are other parallels in antiquity, such as the story of Karna in the Mahābhārata and even Romulus and Remus in the Roman foundation legend.
There are also plenty of usurpers in the history of Egypt and Three "Intermediate Periods", when dynastic lineage was broken or fractured. Scholars have also argued that the Exodus narrative fits within the "Second Intermediate Period", when the Asiatic Hyksos seized control of the Delta.
I remember hearing somewhere that the Egyptians NEVER would have let slaves build the pyramids kind of for a similar reason. This was the kings burial chamber essentially, why would you let slaves touch it in any way and that they would have paid skilled laborers to build it. Not sure if there's any validity to that though. Anyone know if there's any truth to that?