It isn't too silly when one remember that there is no real division between Bereshit and Sh'mot in the Torah. It is continuing a saga.
Also it isn't immediate history either but opera. While based on the historical traditions, Exodus is narrative of the type found in a Haggadah, and in fact most are still to this day directly based on the pattern found within even though it is generally recognized in Judaism that the actual history is different.
The unnamed Pharoah is part of the drama started earlier, acting as the first of a series of adversaries to the fulfillment of the promises made to Abraham, Issac, and Jacob. (Gn 12.2; 13.16; 15:5; 28:14, etc.) It isn't the complete story, either, as it is merely the written tradition arranged from many different traditions of what had be told in Haggadah fashion to direct the Seder along. Passover Seders predate the finished Exodus work, and this of course implies the traditions do as well.
What is missing from the Torah is the tradition that a Redeemer was destined to free the Israelites from bondage and replace the Pharoah as the leader of the inhabitants of Goshen. For this reason the Pharoah is disturbed about losing a large number of his subjects to this unheard of, yet-to-born Redeemer of the Israelites. Thus only the boys are instructed to be killed by Pharoah since it was believed that proper leadership could only be validly exercised by males.
It is unfortunate, but JWs have convinced people that you can read the Scriptures with full comprehension outside their culture. It never works. Remember that Scripture was written to supplement the already functioning Liturgy of Judaism, not act as the foundation for their beliefs. Exodus was written to be proclaimed at worship services, not as a writing upon which to base religious beliefs...unless you still believe what the Watchtower teaches.