Having been born and raised in North America, the concept of a chief rabbi is someone foreign to me. Canada has never had, to my knowledge, such a post. The last person to hold such a title, Rav Avraham Price, zt"l, was the last chief rabbi of Toronto and died in 1994. I don't know if the other two large and old communities, Winnipeg and Montreal, ever had one.
In Israel the post is more political than anything else and others have noted that it is a position of leadership with no followers since the chilonim don't care about what the Chief Rabbi has to say and frum Israelis all have their own rabbonim to ask questions of.
It seems that in Europe there is a much older tradition of having national chief rabbis although again it seems the position is more political, possibly an appointment to be the de facto representative of the Jewish community to the government as opposed to a religious leader.
Is there a place for a chief rabbi nowadays? I would venture that despite the positive examples set by such folks as Rav Jonathan Sacks, there is no real point to having one anymore. There are a few reasons for this.
a) The Jewish community is extremely diverse and, unlike in eras past, not willing to acknowledge the authority of halacha. In the past, there were essentially two types of Jews - those who kept the rules, and those who knew the rules were there but didn't bother keeping them for whatever reason. The more recent innovation of Jewish "streams" that insist they are good members of the faith but predicate their observance on non-obedience to halacha adds a layer of complexity to who can represent the Jewish community. An Orthodox rav cannot speak on behalf of those who do not share his values. A secular leader often does not understand or care about the priorities of the religious community.
b) As I noted above, the position of Chief Rabbi does not carry any religious authority with it. Rav Yosef Eliashiv is, in essence, the Chief Rabbi of the Litvish community. Rav Moshe Sternbuch is the Chief Rabbi of the Mea Shearim community. Rav Shlomo Aviner is the leading Mizrachi authroity. Rav Ovadiah Yosef runs Sephardic Orthodoxy. Each Chasidic clan has its own rebbe to follow and there is no universally recognized authority in the Modern Orthodox community. There is no unifying figure whose psak would cut across "party lines" and be seen as binding on all Torah-observant Jews. Certainly the two current Israeli Chief Rabbis both get their marching orders from other authorities and are glorified followers at best.
Is there any purpose then to maintaining such posts or should they be relegated to the dustbin of history? I would suggest that they should since their continued existence does not add anything to the communityj except a cost for the maintaining of their position.