The House of Jacob is the Israelites. They are the blood descendants of Jacob, the Jewish nation.
The Jews wanted an earthly king.
1 Samuel 8:6 But the thing was displeasing in the sight of Samuel when they said, "Give us a king to judge us." And Samuel prayed to the LORD. 7 The LORD said to Samuel, "Listen to the voice of the people in regard to all that they say to you, for they have not rejected you, but they have rejected Me from being king over them. 8"Like all the deeds which they have done since the day that I brought them up from Egypt even to this day-- in that they have forsaken Me and served other gods-- so they are doing to you also.
1 Samuel 8:19 Nevertheless, the people refused to listen to the voice of Samuel, and they said, "No, but there shall be a king over us
20 that we also may be like all the nations, that our king may judge us and go out before us and fight our battles."
This throne was a throne of the kingdom of God.
1 Chronicles 28:5 Of all my sons--and the LORD has given me many--he has chosen my son Solomon to sit on the throne of the kingdom of the LORD over Israel.
This was the last time there was an earthly king over God's kingdom:
Ezekiel 21:25 “…and thou, profane wicked prince of Israel, whose day is come, when iniquity shall have an end, Thus saith the Lord GOD; Remove the diadem, and take off the crown: this shall not be the same: exalt him that is low, and abase him that is high. I will overturn, overturn, overturn, it: and it shall be no more, until he come whose right it is; and I will give it him.”
Jesus is the righteous one who would set on the throne.
Isaiah 16:5“And in mercy shall the throne be established: and he shall sit upon it in truth in the tabernacle of David, judging, and seeking judgment, and hasting righteousness.”
Amos 9:11“In that day will I raise up the tabernacle of David that is fallen, and close up the breaches thereof; and I will raise up his ruins, and I will build it as in the days of old:”
So we see from the scriptures that the earthly throne of Israel was actually God's throne.
We can see from the scriptures that the Jews wanted a man to sit on that throne.
That does not negate the truth being that THAT THRONE David end up having was God's throne, but on earth because that is what the Jews wanted. They rejected God and chose an earthly king.
Jesus is the righteous one who is NOW SITTING on that throne.
When Jesus comes again, it will be at the resurrection of the dead.
That is the last judgment and when all enemies are put under him.
THEN the NEW JERUSALEM will come down on the NEW EARTH---and Jesus HANDS OVER THE KINGDOM to the Father.
Jesus is Ruler of everything, not just over an earthly Israel.