I'm not sure there's a reason for these *particular* curves to have no points, but I think people expect in general that a "random" high-genus curve over Q has no points; so in a situation like this one one might guess that the curves have "only the points they have to have."  In order to heuristicize about this I suppose you'd start by guessing what proportion of genus-g curves of height at most H had rational points (but already this is a bit sticky, since in large genus curves over Q are presumably concentrated on some unknown proper closed locus in the general-type M_g) and then ask whether this sum converges for the X_{ns}(ell)!