Should the Chief Rabbinate be closed?

You may have read this week that the American Jewish Committee called on the Israeli government to reform the institution of the Chief Rabbinate.
Many would agree with their statement that “In the 21st century, a coercive Chief Rabbinate has become, at best, an anachronism, and, at worst, a force dividing the Jewish people. The role of Israel’s Chief Rabbinate requires significant modifications so as to bring Israel into greater harmony with contemporary democratic norms, particularly as practiced and understood by Diaspora Jewish communities.”
There is much to be said for this statement.  Israel’s rabbinate – in its current form and with its significant power over personal status issues – is a source of contentiousness among Jews both here in Israel and the Diaspora. 
The AJC statement goes so far as to recommend that the Chief rabbinate serve a role similar to the role of the Archbishop of Canterbury. Just as the Archbishop plays a central role in national ceremonies but has little power , and – according to Wikipedia – leads by persuasion, so should be the function of the Chief Rabbi.
I think that this is a good model. But it ignores the difficult questions – ones that I struggle with every day.  For example, without the chief rabbinate, is their civil marriage in Israel? And if so, are we comfortable with the State supporting intermarriage. Each week I speak to couples who seek to get married and who deserve much better than what the State of Israel is able to provide them. When a couple who can’t prove their Jewishness to the satisfaction of the Chief Rabbinate because their grandparent’s documents were thrown out of the window of a cattle car on the way to a concentration camp is told they can’t get married here, I cry with them.  But I also am hesitant to allow for a free for all.
We need not separate religion and State here in Israel. We just need to find a way to speerate religion and politics.