A demographically representative Supreme Court?

I was intrigued by an article in the paper showing the breakdown of the members of the US Supreme Court, prompted by the recent death of Judge Antonin Scalia. It seems that, of the eight remaining judges in the Court, five are Catholic (62.5%), and three are Jewish (37.5%). Before Scalia's death, these percentages were 75% Catholic and 25% Jewish.
A quick check on Wikipedia tells me that, among the general population of the USA, only 24% are Catholic, and 1.7% are Jewish. About 51% are Protestant, other Christians make up another 3%, other religions a further 3%, and 16% have no religion at all (these are 2004 figures). So, does the Catholic-Jewish skew of the Supreme Court reflect the demographics of the legal profession in the USA, because it certainly doesn't reflect the general populace.
Three out of the eight of the current judges are female (was three out of nine), which is getting closer to, but still not quite representative of, the gender demographics. One is black, one is Latino, and the rest are white, which is actually reasonably close to the country's demographic averages, although, out of the full complement of nine judges, two Latinos would better represent the proportion in the general population. Five of the eight were educated at Harvard and three at Yale (was six and three before Scalia's departure), which is probably no surprise, but maybe a rather sad reflection of the way the world works.
Perhaps the most important statistic, though, is that, of the remaining eight judges, four were appointed by Republican presidents and four by Democrats, which probably reasonably fairly reflect the judges' politics too. This, of course, is why the Republicans are making such a fuss about Barack Obama appointing his own choice to the Court so late in his tenure, even though he is well within his rights to do so. A Democratic appointment would swing the political balance Democrat-wards for some years to come. The Republicans, confident that their guy will win the next presidency, want to wait, so that they can swing the balance their way.
It seems to me that what is needed to balance things out, is a female Latino judge (or, better still, an atheist), preferably one with lots of good legal experience, and absolutely no political affiliations, and preferably educated in some little-known backwoods university in Idaho or something. Good luck with that.
Presidential appointment seems a kind of ridiculous way to populate the country's highest court, especially given the influence the Court can have over the way a country operates. But, that is the way it has always been, and, guess what, we do the exact same thing here in Canada too.
A bit of research shows me that four of our nine Canadian Supreme Court judges are female, which apparently qualifies as the world's most gender-balanced national high court, and indeed the Chief Justice (who has slightly more influence in court decisions) is currently Beverley McLachlin, a woman. Full marks so far.
Religious affiliations are harder to glean, but what does jump out is that no fewer than seven out of nine (78%) of them were appointed (technically, nominated) by ex-Prime Minister Stephen Harper. Political balance? I don't think so. Broken system? I think so.