How did the beatitudes create such an impact?

Jesus was showing how the indwelling of the Father works. Later He explained this high concept in John Chapters 14-17, specifically John 14:20 wherein the Father was in Him and later He would be in the disciples, which is how God always comes: in Spirit.

So Jesus was a man speaking the Words of His Father, Father God. No man ever spoke Words on Earth so God-indwelled than Jesus Himself. Inasmuch as religious folk aways want God to come in some utopian manner that prevents Him from doing so (like in corporal body not a person's body thru the spirit), Jesus was saying more or less, "Behold, God-come-in-man speaking directly to you. Any questions?"

When a man-in-God operates at this extremely high level, the impact is at an extremely high level.

Jesus was showing us how to operate In That Day, which now is.