Onsager's solution vs Mean Field Theory

This is a question on the reliability of the Mean Field approach. I have been studying the Ising model recently and have come across 2 approaches to solve the Ising model. For simplicity, I set $k_{B}=1$. The approximate method of Mean Field Theory predicts a point of criticality at

$$beta_{crit}^{MF}=frac{1}{Jz}$$
For the 2D case, $z=4$, so for $J=1$, $beta_{crit}^{MF}=0.25$. But according to Onsager’s exact approach,
$$beta_{crit}=frac{1}{2J}ln{left(sqrt{2}+1right)}$$
resulting in $beta_{crit}approx 0.44$. I realize that Onsager’s approach, being exact, is more accurate, but the deviation between $beta_{crit}^{MF}$ from $beta_{crit}$ seems to be quite large. In which case, what utility can we gain from applying Mean Field Theory?

For example, I am currently working on a more complicated Hamiltonian, and the Mean Field Theory approach fails to accurately predict the critical points, but gets the general trend correct (Based on numerical simulations). This is similar to how $beta_{crit}^{MF}$ and $beta_{crit}$ both predict a $frac{1}{J}$ dependence. Is this normal? Am I correct in saying that Mean Field Theory can predict trends in the phase space but not the exact points of criticality?