In a recent answer you noted that the Jews had to discontinue animals sacrifices in 70
In 2 Chronicles 6:5-6 we’re told that God had designated Jerusalem as the place where His Temple would be located. When the 2nd Temple was destroyed in 70 AD Jerusalem was also destroyed and the people who hadn’t escaped earlier were trapped and died there. Eventually the Romans made it illegal for Jewish people to even enter what remained of the city. It was plowed under by the Romans and a new city called Aleia Capitolina was built over the ruins with a new temple dedicated to Jupiter in place of God’s Temple.
There were no sacrifices during the Babylonian captivity for the same reason as above. Both the 1st Temple and Jerusalem were destroyed in 586 BC and the remaining Jewish population was marched off to Babylon. Ezekiel is sometimes called the father of the synagogue because it was he who instituted that method of worship while they were in captivity.