I've always thought that Pharaoh's dreams had more to them than the interpretation given by Yosef. Indeed, the midrash states that Pharaoh's wise men offered several other interpretations, which he rejected.
Particularly, Pharaoh's dreams could be taken as presaging a fall from power. Pharaoh and his dynasty would be represented by the fat cows and good sheaves of grain, and the subsequent skinny cows and bad sheaves of grain would be a subsequent dynasty, and the new dynasty would replace the previous one such that there was no memory of the previous one. (throwaway line: Just as the new king had no memory of Yosef...) Pharaoh was positioned on the side of the Nile, witnessing the swallowing up, to show that what he was witnessing had direct relevance to him.
Indeed, Yosef's dreams are taken to refer to a rise to power (kingship). And the butler and the baker's dreams are interpreted to refer to whether they will return to their former power of whether they will be executed. When Pharaoh heard the meaning of their dreams as given by Yosef, and how he was accurate, he immediately called for Yosef to interpret his dreams.
Thus, perhaps Pharaoh's dreams were multivalent - they had more than one true interpretation.
There seems to be a midrash that echoes this idea. We read in the parsha how Aaron's staff turns to a tanin (snake, or perhaps crocodile). The magicians do likewise, and then Aaron's tanin swallows up theirs, or perhaps his staff swallows up their staffs.
In Shemot 7:10-12:
tanin - in the haftara of parshat Vaera, he is explicitly called a great tanin. The midrash further says that Pharoah though - if the staff can swallow them, the next thing will be that he will command the staff to swallow me!
But even more, the midrash cites the following statement - that even though the staff swallowed all the other ten staffs, it did not increase in thickness but remained at its previous thickness. This is a deliberate throwback to Pharoah's dream - and is the fulfullment of the dream - of the challenge to Pharaoh's power. To scare Pharaoh even more, Moshe is then commanded to appear to Pharaoh on the bank of the Nile - again, echoing Pharaoh's dream. Shemot 7:15: