How does optimizing the molecular orbital coefficients in CASSCF improve its multi-reference capabilties?
I think you are maybe confusing how dynamical and static correlations are treated with different method. Also CASSCF by itself is not a multi-reference method.
CI in general is able to describe both dynamical and static correlation (FCI does at least). What is treating dynamical correlations (but not static) is the truncation scheme using different degrees of excitation, or example CISD, or in a similar way CCSD. Those are called single-reference methods, because they generate configurations based a single reference wave function.
To deal with static correlations you can for example use the Active Space approach (CASCI), or select configurations by hand (since you might not need to many here).
The term multi-reference refers to doing both, dynamic and static correlation, by generating excitations starting from multiple configurations. One first does a calculation for static correlation (usually MCSCF or CASSCF). Then a second calculation adds dynamical correlations by using the configurations from the first calculation (all or only the most important ones) as multiple reference points (e.g. MRCI-SD or MRCC-SD).
Optimizing the MO coefficients in a MCSCF calculation (e.g. CASSCF) is about optimizing the one-electron basis for your specific CI problem. Since you include more than just one configuration, the HF orbitals are not optimal anymore. In principle you could combine MCSCF with CISD as well, but usually CISD generates to many configurations making such an approach unfeasible.
TL;DR
The optimization of the orbitals in MCSCF does not directly improve the multi-reference capabilities. But it improves the description of static correlation, so you get a better starting point for your multi-reference calculation.
Maybe this explains better the need to optimize both sets of coefficients:

[...] The presence of several important configurations poses a difficult challenge for ab initio electronic-structure theory. The single-configuration Hartree-Fock approximation, by its very construction, is incapable of representing systems dominated by several configurations. By the same argument, methods designed to improve on the Hartree-Fock description by taking into account the effects of dynamical correlation, such as the coupled-cluster and Moller-Plesset methods, are also not suitable for such systems. Furthermore, to carry out a CI calculation 'on top of the Hartree-Fock calculation'is problematic as well since the Hartree-Fock model is inappropriate as an orbital generator: the orbitals generated self-consistently in the field of a single electronic configuration may have little or no relevance to a mutliconfigurational system.
An obvious solution to the multiconfigurational problem is to carry out a CI calculation where the orbitals are variationally optimized simultaneously with the coefficients of the electronic configurations, thereby ensuring that the orbitals employed in the wave function are optimal for the problem at hand and do not introduce a bias (towards a particular configuration) in the calculations. This approach is referred to as the multiconfigurational self-consistent field (MCSCF) method. [...] it may be used either as a wave function in its own right (for a qualitative description of the electronic system) or as an orbital generator for more elaborate treatments of the electronic structure.

Taken from the introduction to the MCSCF chapter in the book T. Helgaker, P. Jorgensen, and J. Olsen. Molecular electronic-structure theory. New York: Wiley, 2000.