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Basically, yes, and yes. A Ph.D in the theory of some field should well qualify you to be a professional theorist. But there really are not hard prerequisites, per se. I've known experimentalists to dabble in theory, and conversely.
Said similarly, the ergodic hypothesis I believe is a statement that the a closed Hamiltonian system specified by a phase representative point will evolve to (or arbitrarily close to) any accessible microstate given sufficient time. It's a nice development of Liouville's theorem if I am not mistaken.
The way this was presented to me in my undergraduate E&M course (Wangsness' Electromagnetic Fields) is that you can treat the straight segment as a closed loop if you consider the parallel segments to be infinitely far apart such that their contributions to the line integral fail to contribute at all field points in your calculation/region of interest. I don't care for the reasoning much myself though, it seemed a bit crude to me then and now even moreso that I'm remembering it. I asked the same question as I recall.
+1 for this analogy. I've never heard it before, is it in his lectures? I can't render the link on my phone, but I'll use it when I next present this introductory material for certain!
@CuriousOne All that I'm saying is that the possibility of the OP wanting of a discussion/explanation of the cause of this particular phenomenon rather than simply being content with knowing the observable effect seems to be honorable. What good is a measurement if we can't make sense of it? In any case, don't misinterpret me for a theologian. You mentioned philosophy - I'd suggest you revisit the phrase "higher implications" in the context of what the OP is asking and in that of your own comment.
@CuriousOne but who's to say that such philosophical and scientific/empirical reasoning ought to be entirely disjoint? I definitely understand where you're coming from, but I also think that it is necessary (and respectable) for one to consider higher implications of empirical results. Whether such a stance was the OP's intention though, I can't say.
