  We study the large-Q^2 behavior of the meson form factor F_M (Q^2)
constructed using the holographic light-front wave functions proposed recently
by Brodsky and de Teramond. We show that this model can be also obtained within
the Migdal's regularization approach (``meromorphization''), if one applies it
to 3-point function for scalar currents made of scalar quarks. We found that
the asymptotic 1/Q^2 behavior of F_M (Q^2) is generated by soft Feynman
mechanism rather than by short distance dynamics, which causes very late onset
of the 1/Q^2 asymptotic behavior. Using meromorphization for spin-1/2 quarks,
we demonstrated that resulting form factor F^{spinor}_M (Q^2) has 1/Q^4
asymptotic behavior. Now, owing to the late onset of this asymptotic pattern,
  F^{spinor}_M (Q^2) imitates the 1/Q^2 behavior in the few GeV^2 region.
  We discuss analogy between meromorphization and local quark-hadron duality
model for the pion form factor, and show that adding the O(\alpha_s) correction
to the spectral function brings in the hard pQCD contribution that has the
dimensional counting $1/Q^2$ behavior at large Q^2. At accessible Q^2, the
O(\alpha_s) term is a rather small fraction of the total result. We conclude
that the ``observed'' quark counting rules for hadronic form factors is an
approximate phenomenon resulting from Feynman mechanism in its preasymptotic
regime.
