This is methinks a Christian perspective; not necessarily, however, the only Christian perspective. As Kaninchen has hinted, the Temple was not the beginning nor the end of Judaism (and neither is the Messiah) since many Jews could not even travel to the Temple. So-called rabbinic Judaism in the form of local synagogues was already in place while the Temple existed. In fact, many Jews were already cut off from the Temple after its FIRST destruction by the Babylonians. Further, blood offerings were not the only means of atonement for sins, especially for those who were poor and those who had no access to the Temple: flour offerings were perfectly acceptable. Besides, blood atonement or sacrifices were only for the purpose of UNINTENTIONAL sins, not intentional sins; and thus, blood sacrifices were the WEAKEST means of atonement, while prayer and good deeds are the strongest. The Hebrew Bible is quite clear regarding all of this. Finally, the so-called judgment you speak of enabled the Jews to disperse throughout many nations and bring their religion and ethical values with them. They were influenced by some of the customs in foreign lands but they also influenced others to adopt more ethical values.
Here is my real response.
The sacrifice being for unintentional sins only is carried into the New Testament. What is to be understood as “unintentional” is committing sin without the desire to deliberately break God’s commandments and go against him. This is carried over into the New Testament as well and also applies to the sacrifice of Christ.
“If we deliberately keep on sinning after we have received the knowledge of the truth, no sacrifice for sins is left,” - Hebrews 10:26
“but whoever blasphemes against the Holy Spirit will never be forgiven; they are guilty of an eternal sin.” - Mark 3:29
The New Testament also puts as much stress on repentance and good deeds and prayer as much as the Old Testament does.
“Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven.” - Matthew 7:21
“But love your enemies, and do good, and lend, expecting nothing in return; and your reward will be great, and you will be sons of the Most High; for He Himself is kind to ungrateful and evil men.” - Luke 6:35
“Peter replied, ‘Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit.’” - Acts 2:38
“Repent therefore and be converted, that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord,” - Acts 3:19
“Truly, these times of ignorance God overlooked, but now commands all men everywhere to repent,” - Acts 17:30
“First to those in Damascus, then to those in Jerusalem and in all Judea, and then to the Gentiles, I preached that they should repent and turn to God and demonstrate their repentance by their deeds.” - Acts 26:20
“Do not marvel at this; for an hour is coming, in which all who are in the tombs will hear His voice, and will come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment.” - John 5:28-29
“But because of your stubbornness and unrepentant heart you are storing up wrath for yourself in the day of wrath and revelation of the righteous judgment of God, who will render to each person according to his deeds: to those who by perseverance in doing good seek for glory and honor and immortality, eternal life;” - Romans 2:5
“Instruct those who are rich in this present world not to be conceited or to fix their hope on the uncertainty of riches, but on God, who richly supplies us with all things to enjoy. Instruct them to do good, to be rich in good works, to be generous and ready to share, storing up for themselves the treasure of a good foundation for the future, so that they may take hold of that which is life indeed.” - 1 Timothy 6:17-19
“What use is it, my brethren, if someone says he has faith but he has no works? Can that faith save him? If a brother or sister is without clothing and in need of daily food, and one of you says to them, “Go in peace, be warmed and be filled,” and yet you do not give them what is necessary for their body, what use is that?” - James 2:14
“For as the body without the spirit is dead, so faith without works is dead also.” - James 2:26
“Therefore confess your sins to each other and pray for each other so that you may be healed. The prayer of a righteous person is powerful and effective.” - James 5:16
“Consider how far you have fallen! Repent and do the things you did at first. If you do not repent, I will come to you and remove your lampstand from its place.” - Revelation 2:5
“Repent therefore! Otherwise, I will soon come to you and will fight against them with the sword of my mouth” - Revelation 2:16
“Therefore, I will throw her on a bed of suffering, and those who commit adultery with her will suffer greatly unless they repent and turn away from her evil deeds.” - Revelation 2:22