This is not correct reasoning. Of course, God could harden anybody, we all acknowledge and understand this. But in Romans 9-11, Paul is clearly focusing on Jews and how Jews have been hardened. Yes, Paul refers to Pharaoh as being hardened. But this is an example of God's right to harden and it is deployed in this section as one of many examples leading to Paul's overall conclusion - God has hardened Jews for the benefit of Gentiles.Here is the problem with your analysis above. It contains a partial truth. The partial truth is that Israel is the primary focus in chapters 9-11. However, Israel is only the PRIMARY focus not the ENTIRE focus because salvation or hardening cannot be limited to merely Israel in exclusion of the Gentiles.
The fact that God could harden Gentiles obviously does not mean that Paul is not permitted to make an argument about how God has specifically hardened Jews for a specific redemptive purpose.
The problem with your position is this: First, we read in chapter 9 about "vessels of destruction being hardened". Let's say that we agree that we provisionally conclude that there is no "Jew-specificity" here - that Paul is talking about Gentile as well. But when we get to this passage, clearly directed at the Jew, we should clearly get the point that he is talking about Jews being hardened, and only Jews:
What then? What Israel is seeking, it has not obtained, but those who were chosen obtained it, and the rest were hardened;
8just as it is written,
"(M)GOD GAVE THEM A SPIRIT OF STUPOR,
EYES TO SEE NOT AND EARS TO HEAR NOT,
DOWN TO THIS VERY DAY."
9And David says,
"(N)LET THEIR TABLE BECOME A SNARE AND A TRAP,
AND A STUMBLING BLOCK AND A RETRIBUTION TO THEM.
10"(O)LET THEIR EYES BE DARKENED TO SEE NOT,
AND BEND THEIR BACKS FOREVER." 11(P)I say then, they did not stumble so as to fall, did they? (Q)May it never be! But by their transgression (R)salvation has come to the Gentiles,
Paul is quoting Old Testament texts that refer to the hardening of Israel here. I can make the case in more detail but the overall context of 9-11 really does drive us in the direction in seeing the vessels of destruction as hardened Jews. Otherwise, we have Paul talking about the tragedy of hardened Israel all throughout the 9 to 11 block, and yet mysteriously going off on a tangent in the middle of chapter 9 to make a case about "hardening" that has no Israel specificity whatsoever.
Competent writers do not do that. And Paul is most clearly a very competent writer.