Herod wanted to be remembered for something else.
He wanted to be remembered as the man of influence - friend of Julius Caesar, Mark Antony, and Augustus. He wanted to be remembered as a political prodigy: governor of Galilee by age 25, Roman governor of Coele-Syria, tetrarch of Judea. He wanted to be remembered as "King of the Jews" - a title bestowed on him by a vote of the Roman Senate, despite the fact that he was neither royal nor Jewish. He wanted to be remembered as a successful commander: he defeated the brigand Ezekias in his youth, and he commanded a Roman legion to reclaim Israel from the Parthian empire.
Herod wanted to be remembered for his public works. He had a thousand Levites trained as stone masons to totally refurbish the Temple. He built aqueducts, baths, fortifications, hippodromes, theatres, amphitheatres and gymnasiums, not only in Israel but in other nations. He built a shrine to Augustus and allowed a statue of himself to be erected in another temple - not something that endeared him to his Jewish subjects. He built the port and city of Caesarea Maritima, still an amazing feat.
Herod wanted to be remembered for his generosity towards his subjects. He twice reduced taxes, once by one-third and once by one-fourth. During a famine, Herod sold the silver in his palace to provide food for his people.
Herod wanted to be remembered for his protection of Jews throughout the Roman Empire. Because of Herod's influence with Augustus, Jews throughout the Empire gained official protection: they could not be compelled to appear in court on the Sabbath; they were exempt from having to participate in Roman religious rituals; and shipments carrying their annual head-tax to the Temple were protected by Roman law and Roman might.
But Herod is remembered for none of these things by most people. Instead, Herod is remembered only for how he responded to the baby Messiah. His brutality in killing the baby boys of Bethlehem was unfortunately entirely consistent with his character. Although Herod killed many, those who could make a more legitimate claim to kingship than Herod were his special targets. He killed most of the remnants of the previous royal dynasty, the Hasmoneans, including his own wife and sons. It is not surprising that Herod would also try to kill the offspring of an even older dynasty, the Son of David.
By the way, don't get your Herods confused. Herod the Great was king of Israel (40-4 BC), and is famous for trying to kill the baby Jesus (Matt 2:16). Herod Antipas, his son, was tetrarch of Galilee (4 BC - AD 39), and is famous for executing John the Baptist (Matt 14:3-12) and interrogating Jesus (Luke 23:6-12). Herod Agrippa I, grandson of Herod the Great, ruled over Israel (AD 37-44), and is famous for executing James the son of Zebedee and being eaten by worms (Acts 12). Four other family member show up in the NT: Archelaus, ethnarch of Judea, son of Herod the Great (4 BC-AD6, Matt 2:22); Herodias, granddaughter of Herod the Great and wife of Herod Philip and Herod Antipas (Matt 14:1-12); Herodias' daugher; and Herod Agrippa II, tetrarch of Iturea (Acts 25:13-26:32).
The picture: a coin minted under Herod the Great.