It is always difficult (and dangerous) to try to guess WHY God did something a certain way and not another. Our little minds will never be able to understand the undefinable wisdom of God. Having said that, let's have a go anyway!

Perhaps the reasons that so few people knew of the birth of Jesus might have included:

1. He was meant to remain in hiding until He began His ministry at the age of 30. However, such a huge miracle as the Incarnation of the Son of God could not go unmarked by heaven - hence the heavenly choir.

2. This 'hiding' may have been to protect Him, both from the devil and from those evil people of the world like Herod who would have wanted to kill Him before He had the chance to preach or do miracles or gather Disciples etc. That would have nipped the Christian Church in the bud and stopped it from ever forming!

3. This 'hiding' may also have been to prevent other people giving Him excessive worldy glory, such as those who wished to make Him a worldy king over Israel. Such a unique young man would have certainly caught people's attention, as He did when He visited Jerusalem at the age of 12 and debated with the teachers in the Temple.

Why did God allow those specific people to know about His birth?

It is possible that they were representative of the human race:

Shepherds Wise Men
Poor Wealthy
Hebrew Gentile (non-Hebrew)
God's people Worshippers of other gods
Simple Highly educated
Near Far

...and so on.

It is not strange that God should use the stars to tell the Wise Men about the birth of Christ - God is Lord over all the universe and He is quite able to use the 'language' that they could understand. We also find God using a medium, the witch of Endor, to deliver his message to King Saul when he had left God and followed the wrong paths. Even demons confessed that Jesus is the Son of God when He confronted people possessed by them.

So God, as Lord of the whole creation, can use anyone or anything He wants to achieve His purposes!