You need to notice that in the passage you quoted, Romans 10:16-21, does not say that the Jews had the ability to choose God. God shows patience toward the lost, even those that claim to have free will to choose God, but the time of patience will come to an end, and at that time the wrath of God will fall upon the people who claim to do the opposite of that which Lord Jesus said (John 15:16).
Apparently, you missed this:
He chose Abraham to birth Israel. Out of these ppl the Messiah would come. But it is not as though the word of God has failed. For they are not all Israel who are descended from Israel;[Romans 9:6] Not every Jew was God's elect. (that's a quote from SovereignGrace's post).
Only a fool would write that election is not for salvation. Elect and chosen are the same thing.
Lord Jesus said:
"For many are called, but few [are] chosen."
(Matthew 22:14)
"you did not choose Me, but I chose you"
(John 15:16)
In case you are not sure, still, behold, Lord Jesus said:
"apart from Me you can do nothing"
(John 15:5)
That's a lot to chew on about election, and here is more,
"The Righteous Sovereignty of God Post" (in this thread),
"The Audience of Lord Jesus for John 14:16 and John 15:16 Are All Dicsiples In All Time Post" (in this thread), and
"Matthias and Joseph in Exhibit 7 with the Lord Jesus and the Apostles 'All the Time' Post" (in this thread) contain the Truth.