Ok, but the fact that kosher rights were “first to the party” does not inform us about whether they are the optimum solution; at most, to the fact that their position, given that we have globally approached it over the years, might be partially good.

And, as you touch upon, religious rites do not (solely) search for the solution that is most humane for the animal; they also take into consideration the religious value of the experience for third parties. But that means that, all else being equal, secular slaughtering processes, as they do not seek ritual values, should be more free to converge to the most humane solution.