רש"י suggests that Pharaoh's astrologers told him that they had a vision that a savior would be born on a certain day (שמות א:כב & שמות א:טז). Assuming the “astrologers” had no real power of prediction, what cause the astrologers to make up such a declaration? What was their plan?
Again, my premise is that they had no real power of prediction. I understand one may have the possibility that they had some power of Astrology, but for the purposes of this question I am taking the premise that they had no magic powers.
Beyond our current knowledge of the way the world works, there are many Rishonim that hold astrology and magic are not real. They hold that people often used these things to trick people into following them or their religion. They held there is not basis to astrology, talking to the dead, bad signs or omens etc. I have been asked to provide a source, so I have included one below.
The Rambam says this pretty explicitly in הלכות עבודה זרה פרק י"א הלכה טז:
טז. ודברים האלו כולן דברי שקר וכזב הן והם שהטעו בהן עובדי כוכבים הקדמונים לגויי הארצות כדי שינהגו אחריהן ואין ראוי לישראל שהם חכמים מחוכמים להמשך בהבלים אלו ולא להעלות על לב שיש תועלת בהן שנאמר כי לא נחש ביעקב ולא קסם בישראל ונאמר כי הגוים האלה אשר אתה יורש אותם אל מעוננים ואל קוסמים ישמעו ואתה לא כן וגו' כל המאמין בדברים האלו וכיוצא בהן ומחשב בלבו שהן אמת ודבר חכמה אבל התורה אסרתן אינן אלא מן הסכלים ומחסרי הדעת ובכלל הנשים והקטנים שאין דעתן שלימה אבל בעלי החכמה ותמימי הדעת ידעו בראיות ברורות שכל אלו הדברים שאסרה תורה אינם דברי חכמה אלא תהו והבל שנמשכו בהן חסרי הדעת ונטשו כל דרכי האמת בגללן ומפני זה אמרה תורה כשהזהירה על כל אלו ההבלים תמים תהיה עם ה' אלהיך:
"All the above matters are falsehood and lies with which the original idolaters deceived the gentile nations in order to lead them after them. It is not fitting for the Jews who are wise sages to be drawn into such emptiness, nor to consider that they have any value as [implied by Numbers 23:23]: "No black magic can be found among Jacob, or occult arts within Israel." Similarly, [Deuteronomy 18:14] states: "These nations which you are driving out listen to astrologers and diviners. This is not [what God... has granted] you."
Whoever believes in [occult arts] of this nature and, in his heart, thinks that they are true and words of wisdom, but are forbidden by the Torah, is foolish and feebleminded. He is considered like women and children who have underdeveloped intellects.
The masters of wisdom and those of perfect knowledge know with clear proof that all these crafts which the Torah forbade are not reflections of wisdom, but rather, emptiness and vanity which attracted the feebleminded and caused them to abandon all the paths of truth. For these reasons, when the Torah warned against all these empty matters, it advised [Deuteronomy 18:13]: "Be of perfect faith with God, your Lord."
See the entire פרק for his treatment of these matters.