For the same argument, one could ask: has God kept the Gentiles outside of His covenant people, and then send them to hell?
So regarding the part that is blinded. God blinds them - concludes them in unbelief for the sake of us Gentiles - and then send them to hell?
That is why Paul says: "unsearchable are his judgments" etc. (end Rom 11). In fact, Paul discusses this exact question in Rom 9. God basically hardened their hearts after they already rejected Him. Also in Rom 11:20 "because of unbelief they were broken off"
And it is not as if all Jews were mere marionettes in the hardening, for many did believe (e.g. Nicodemus, Paul) and are still believing today. And many of them are still coming to faith in Christ. (Those that still expect a political, earthly Messiah stay disillusioned). Thats why Paul also says:
Rom 11:22-23 "Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off. (23) And they also, if they abide not still in unbelief*, shall be graffed in: for God is able to graff them in again."
* if they believe
Joh 8:32 "And you shall know the truth, and the truth shall make you free."