Serre relates that early in the sixties, at the IAS, Shimura asked him: "is it true that the L-function of every elliptic curve over $\mathbb{Q}$ is modular" and he replied "why would it be so?". Serre goes on explaining that a question like that is of little value (not even worth of being called a conjecture) if not motivated by either strong evidence or philosophical reasons. It is even an important point in his argument that the name of Weil really belongs in the name of the Shimura-Tanyama-Weil conjectue, as Weil provided both (according to Serre): (1) the observation that there was no Elliptic curve over $\mathbb{Q}$ of small conductor, related to the absence of cuspidal modular forms of weight 2 of small level (with the same precise sense of "small"), and (2) as mentioned by Emerton, Weil's converse theorem, that if the L-function of an elliptic curve say, with enough of its twists, satisfy the basic behavior we have come to expect from all kind of L-functions sine Riemann (analytic continuation and functional equation) then they are modular. Actually, what Weil's result proves is that those nice behavior is essentially the same thing as being modular.

I said the above because you're in the same state of mind than Serre was (in the early sixties). But he became satisfied with the conjecture in the early seventies, after Weil's work on it. Right now I am not sure we have made so much progress in understanding why philosophically those higher reciprocity law should be true. We have a lot of evidence, provided by the huge numbers of particular cases and anlig cases (e.g. the function field case solved by Lafforgue) we have solved. But the main philosophical reasons we believe such things should hold are the same they were then, namely the ones Emerton has recalled, Weil's converse theorems.

We might get a deeper understanding of why those things hold when we eventually prove everything we want in the Langlands program. For some (cf. some philosophical texts by Michael Harris on his webpage, this is even the main interest in proving things in mathematics. But even this is perhaps to optimistic.

Serre relates that early in the sixties, at the IAS, Shimura asked him: "is it true that the L-function of every elliptic curve over $\mathbb{Q}$ is modular" and he replied "why would it be so?". Serre goes on explaining that a question like that is of little value (not even worth of being called a conjecture) if not motivated by either strong evidence or philosophical reasons. It is even an important point in his argument that the name of Weil really belongs in the name of the Shimura-Tanyama-Weil conjectue, as Weil provided both (according to Serre): (1) the observation that there was no Elliptic curve over $\mathbb{Q}$ of small conductor, related to the absence of cuspidal modular forms of weight 2 of small level (with the same precise sense of "small"), and (2) as mentioned by Emerton, Weil's converse theorem, that if the L-function of an elliptic curve say, with enough of its twists, satisfy the basic behavior we have come to expect from all kind of L-functions sine Riemann (analytic continuation and functional equation) then they are modular. Actually, what Weil's result proves is that those nice behavior is essentially the same thing as being modular.

I said the above because you're in the same state of mind than Serre was (in the early sixties). But he became satisfied with the conjecture in the early seventies, after Weil's work on it. Right now I am not sure we have made so much progress in understanding why philosophically those higher reciprocity law should be true. We have a lot of evidence, provided by the huge numbers of particular cases and analog problems (e.g. the function field case solved by Lafforgue) we have solved. But the main philosophical reasons we believe such things should hold are the same they were then, namely the ones Emerton has recalled, Weil's converse theorems.

We might get a deeper understanding of why those things hold when we eventually prove everything we want in the Langlands program. For some (cf. some philosophical texts by Michael Harris on his webpage), this is even the main interest in proving things in mathematics. But even that is perhaps too optimistic.