(Full disclosure: I live in Modi'in, and regularly attend shiurim from Chief Rabbi Lau, and a lot of my opinion is based on comments or observations I have heard from him)
One of the common misnomers is that the Rabbanut doesn't represent anybody, not the Charedim, not the secular, and not even the National Religious community.
This is simply not true. It is true that most Charedim do not respect the institution of the Chief Rabbanut, in much the same way they don't respect many Zionist institutions, however in the Religious Zionist world, there is a strong segment which not only respects the institution of the Chief Rabbanut, but regards it as a critical corner stone of Zionism and the redemptive process.
Rabbi Gil Student has an excellent article on the topic, here is a key quote:
Religious Zionists, particularly among the Chardal, see the Chief Rabbinate in messianic terms. We pray three times a day in the Amidah for the return of the centralized religious judicial system. The Chief Rabbinate is not the fulfillment of that prayer but its precursor. It represents a step in the flowering of the Redemption. Seen in those terms, undermining the Chief Rabbinate is forestalling Mashiach.In other words, while it is true that in Galut, each shtetle, community, or congregation appointed its own rabbi (although many cities and countries also had a Government-recognized Chief Rabbi), now that we are building a Jewish nation, just like we have a centralized, government-recognized Jewish army, police force, court system, education system, medical system, postal system etc, we should have a recognized Rabbanut. This was the vision of Rav Kook when he established the Rabbanut before the state.
None of these government institutions are perfect, many need restructuring or fixing, however there is a difference between fixing a poorly run government institution, and calling for it to be disbanded.
In addition to the ideological principle of having a single uniting rabbanut, there are practical advantages.
Having a centralized record of marriage and divorce is of enormous benefit. If you have ever met a Ba'al Tshuva from Chutz L'Aretz trying to determine whether he is Jewish according to Halacha you would understand why.
If the person comes from England, or any other country with a centralized Rabbanut, provided that their parents or grandparents had a Jewish wedding registered through the Rabbanut (and the vast majority of UK Jews do, even today), it is very easy to get a copy of the Ketuba and details of the Rabbi who conducted the wedding and verify their halachic status.
In contrast, with a Jews from the US, unless they know exactly where and when their grandparents got married, and the Rabbi or community where the grandparents got married is still around and maintains accurate records, it is extremely difficult, and some times even impossible to confirm their halachic status 2 generations later.
There are many other areas where we benefit from a government recognized and funded rabbanut.
In Chutz La'retz Jewish services such as burial, eruv, mikva, marriage registration, and beit din, if they exist at all are privately funded by a congregation, and often individuals who are not members of a congregation are denied these services; many Jews belong to a congregation just so they are entitled to a Jewsih Burial.
Here in the Jewish State almost every city has an eruv, every Jew is entitled to be buried according to Halacha, and there is a Beit Din or Possek available to everyone. Who would be responsible for maintaining these services if we did not have a recognized Beit Din.
With regard to marriage. Personally I am in favour of recognizing civil marriage, in the same way that the government recognizes civil marriage performed abroad. However if individuals want a Jewish wedding, not a civil wedding, weddings should be under the auspices of the Rabbanut and the Rabbanbut should maintain records. I believe that like in England, the vast majority of Israelis would prefer a Halachic wedding, and would want to be able to prove that their future children and grandchildren a Jewish without any question.
With regard to kashrut, there is also a benefit to the kosher consumer knowing that legally an institution can only call itself kosher if it meets a minimum recognized standard of kashrut.
There are big problems in the kashrut industry now, and different Rabbanuts do have different policies or levels of efficiency, and this should be standardized - but removing any level of control and letting anyone advertise themselves as kosher without any supervision at all, is a step in the wrong direction.
In recent years there were real problems with Charedim who did not recognize the Rabbanut taking over key positions, and that was to the detriment of the entire institution, however since Rabbi Lau took over, there has been a definite move to reform the Batei Din, Kashrut supervsion, city eruvin, and other institutions under the umbrella of the Rabbanut.
May these changes continue, and may the office of the chief rabbanut return to the respected position that it deserves, and may the individuals involved be worthy of their office and turn the institution into a Kiddush Hashem.