  We revisit the global existence of solutions with some large perturbations to
the incompressible, viscous, and non-resistive MHD system in a
three-dimensional periodic domain, where the impressed magnetic field satisfies
the Diophantine condition, and the intensity of the impressed magnetic field,
denoted by $m$, is large compared to the perturbations. It was proved by
Jiang--Jiang that the highest-order derivatives of the velocity increase with
$m$, and the convergence rate of the nonlinear system towards a linearized
problem is of $m^{-1/2}$ in [F. Jiang and S. Jiang, Arch. Ration. Mech. Anal.,
247 (2023), 96]. In this paper, we adopt a different approach by leveraging
vorticity estimates to establish the highest-order energy estimate. This
strategy prevents the appearance of terms that grow with $m$, and thus the
increasing behavior of the highest-order derivatives of the velocity with
respect to $m$ does not appear. Additionally, we use the vorticity estimate to
demonstrate the convergence rate of the nonlinear system towards a linearized
problem as time or $m$ approaches infinity. Notably, our analysis reveals that
the convergence rate in $m$ is faster compared to the finding of Jiang--Jiang.
Finally, a key contribution of our work is the identification of an integrable
time-decay of the lower dissipation, which can replace the time-decay of lower
energy in closing the highest-order energy estimate. This finding significantly
relaxes the regularity requirements for the initial perturbations.
