Can we make a massive non-abelian gauge field renormalizable by gauge fixing without Higgs mechanism?

Question

There have been a lot of similar questions about this topic on this website, such as Gauge invariance is just a redundancy. Why is massive abelian gauge field renormalizable but massive non-abelian gauge field nonrenormalizable?. We know the propagator of massive vector field is like \begin{equation} -i\frac{g_{\mu \nu}-k_{\mu}k_{\nu}/m^{2}}{k^{2}-m^{2}}. \end{equation} And we know the propagator behaves as $O(1)$ at high momentum, so the power counting law breaks down and the theory is non-renormalizable.
However, I wonder, can we mimic what we do for $U(1)$ field: there we introduce gauge fixing by Faddeev-Popov method, then we get something like \begin{equation} \frac{-i}{k^{2}-m^{2}}(g_{\mu \nu}-(1-\xi)\frac{k_{\mu}k_{\nu}}{k^{2}-\xi m^{2}}) \end{equation} (see this notes (62), but here I am NOT talking about Higgs mechanism, I just cite the calculating result of gauge fixing for massive boson field.)
By letting $\xi$ equal 1, we get \begin{equation} \frac{-ig_{\mu \nu}}{k^{2}-m^{2}}. \end{equation}
It seems that we can solve the $O(1)$ difficulties at high momentum and it is renormalizable for the massive non-abelian gauge field. I wonder if this idea makes any sense?