  We study the leading coefficient in the asymptotical formula $ N (R) =
\frac{W}{\pi} R + O (1) $, $ R \to \infty $, for the resonance counting
function $ N (R)$ of Schr\"odinger Hamiltonians with point interactions. For
such Hamiltonians, the Weyl-type and non-Weyl-type asymptotics of $N (R)$ was
introduced recently in a paper by J. Lipovsk\'y and V. Lotoreichik (2017). In
this note, we prove that the Weyl-type asymptotics is generic.
