I commend to readers the first two comments posted on Trevor's post, which make very good points. Here are a few further thoughts:
1) I continue to think that in general the call for non-lawyers on the Court emanates from a right-wing populist attack on the perceived liberalism of the Court. I'm not calling Vermeule either right-wing or populist. He's making an academic proposal, which is something else altogether. As an aside, it's notable that lawyer-bashing is a common form of right-wing populism, while the idea of the heroic lawyer standing up for the little guy is a common form of (American) left/liberal populism. (Think Erin Brockovich, John Edwards, etc.)
2) The weak form of Vermeule's proposal--inter-disciplinary Justices--cuts against the populism and anti-lawyer cast of the strong form. Those with PhD's as well as JD's are likely to be even more remote from the values of the volk than plain old lawyers. This would hardly satisfy Scalia's opposition to the "lawyer class" as expressed in his Romer dissent.
3) So we can understand the weak Vermeule position as sounding in technocracy, whereas the strong version sounds in populism. It's curious to marry these positions to one another--although early 20th century Progressives tended to be both populists and technocrats. Vermeule, for what it's worth, is a fan of Dewey, so who knows? Maybe he wants to reconnect these strands. ("Democratic experimentalism" of the sort I have offered in some of my academic work also seeks to recapture these connections.)
4) Historically and still today, our legal system has received democratic input principally in two places: a) electoral representation; and b) juries. The notion that the law interpreters should also be in touch with popular sentiment as well likely reflects the trickling down to the general population of legal realism.