Your Honor, Chief Rabbi Yitzchak Yosef,
You are correct!
The Law of Return creates many problems. Until the 1970 amendment, it was clear that any Jew who made Aliya to Israel, since their family was persecuted because of their Judaism, since they are part of the public identified as Jewish in the Diaspora, is also Jewish in Israel. But then the law was changed to distinguish two groups of Jews: (1) those whose mother was Jewish or they were converted; (2) family members of Jews.
If you meet them on the street, you won’t know how to distinguish them. Between us, if you meet the children and grandchildren of those immigrants, you will not be able to point out any difference between them and other secular Jews. Secular-Jews are, of course, Jews according to the highest standard and secular according to the highest standard.
But, as you said, anyone who happened to only have a Jewish grandfather is listed in Israel as lacking religion and they are denied the right to marry as a Jew in Israel and to be buried as a Jew in Israel. Not because they would not want to register as a Jew, but because the State of Israel does not allow them. Because the rabbinate and the religious parties insist on not allowing them.
In contrast, anyone who happened to only have a Jewish grandmother—even if they immigrated together, led the same lifestyle, and voted for the same parties—are registered as a Jew without anyone testing their beliefs and lifestyles, and they are entitled to marry and be buried by rabbis like you.
Why? Because! For that is how halakhah, apparently, and only apparently, decides.
The Chief Rabbi of Israel is not supposed to be the Chief Rabbi of the Shas Movement, nor is he the Chief Rabbi of religious Jews only. He is supposed to be the Rabbi of the State of Israel. This was the way your father, Rabbi Ovadia Yosef Z”l, presided over the Chief Rabbinate and faced national challenges.
The Citizens of the State of Israel understand that everyone who immigrated under the Law of Return is Jewish. It is upon the Chief Rabbinate of the State of Israel to solve this problem: to convert all immigrants quickly, allow them to register as Jews, grant them the rights granted to every Jewish citizen.
Halakhah has the tools to do it.
If the current rabbinate is not up to the task—it must be replaced—not the Jewish people.