Another way of putting it is that there are many good ways of doing project management, as many good ways as their are unique (team, circumstance) pairs.
Most people have an intuitive understanding of why some very low-overhead, low-formalism, "just get stuff done and be reasonable" workflow has worked really well in some specific (team, circumstance) combo situation.
If you want them to override their experiences with how those ad hoc, customized management processes worked well, and instead believe that a company-wide, one-size-fits-all approach that removes tons of workflow autonomy that could just be left up to separate teams to customize for themselves, then you absolutely have to have extremely convincing answers to address widespread bad experiences.