**No it does not.**
Yes. It does. He singles out the Pharaoh and they reason he hardened his heart. You are right that it is families (covenantal) and but it is individual. Clear as the nose on your face. (I am assuming you have one.)
Tell me something. Surely you know someone that is very close to you that doesn’t believe. Do you pray that they will come to faith?
Egypt was ‘in Pharaoh’, and all of Egypt suffered punishment.
“For the Scripture says to Pharaoh, For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth. 18 So then he has mercy on whomever he wills, and he hardens whomever he wills.”
When God hardens a heart, he does not reverse the desire of the heart. “And since they did not see fit to acknowledge God, God gave them up to a debased mind to do what ought not to be done.” In essence, God hardens a heart by shoving it further in the direction it already wants to go. But all Egypt was in Pharaoh as its head, and Egypt received the punishment as well as Pharaoh. Thus we see CORPORATE guilt, with Pharaoh being the head - as Jesus becomes our head, if we believe and are grafted into him.
But Romans 9 is clearly discussing Jew corporately - while individual Jews had followed Jesus, the majority did not. Why, and what would happen to them?
And the answer Paul gives is:
” Why? Because they did not pursue it by faith, but as if it were based on works. They have stumbled over the stumbling stone, 33 as it is written,
Behold, I am laying in Zion a stone of stumbling, and a rock of offense;
and whoever believes in him will not be put to shame.
The Jews were complaining that they were already God’s Chosen People, and that they did not need faith. But Paul points out that faith had always been needed, from Abraham on, and that God had the right to set the condition of faith.
He continues his argument in Romans 10, and finishes in Romans 11 with:
“17 But if some of the branches were broken off, and you, although a wild olive shoot, were grafted in among the others and now share in the nourishing root of the olive tree, 18 do not be arrogant toward the branches. If you are, remember it is not you who support the root, but the root that supports you. 19 Then you will say, Branches were broken off so that I might be grafted in. 20 That is true. They were broken off because of their unbelief, but you stand fast through faith. So do not become proud, but fear. 21 For if God did not spare the natural branches, neither will he spare you...And even they, if they do not continue in their unbelief, will be grafted in, for God has the power to graft them in again. 24 For if you were cut from what is by nature a wild olive tree, and grafted, contrary to nature, into a cultivated olive tree, how much more will these, the natural branches, be grafted back into their own olive tree.”
In Christ, a gentile is grafted in if he believes. But a Jew who refuses to believe will be cut off. But if that Jew then believes, he will be grafted back on. It is BELIEF that determines the outcome, not saying, “But God has chosen me!”
As for prayers for the lost, I ask God to reveal Himself to them in a clear & explicit fashion. But I also understand that God will not force them to believe, and that a man may hear the Gospel, have had every chance to believe, and yet not do so. When you give someone the right to choose, then their choice becomes significant.
Some people meet this description: “For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened...Though they know God’s righteous decree that those who practice such things deserve to die, they not only do them but give approval to those who practice them.”