Why would it be bad for philosophy to work (primarily) with intuitions? And why would philosophy need empirical evidence? (Relating to the point in the linked post on criticism of dualists not having any evidence). Empirical evidence is not what is (primarily) used in mathematics. If everything could be solved with empirical evidence, there would be no need for philosophy.
I don’t see how scientific evidence is better than intuition. Or even possible without them...
In case you mean not only empirical evidence but also logical/ mathematical (?) evidence: Why is intuition not also evidence itself, i.e. why not let it be a PART of the reasoning?
Also I don‘t get why we would need training in cognitive sciences. What do you mean that the brain is the tool and we need to know how to use it? What will it help my reasoning to know how neural networks are connected (for example)? And why is it necessary? (To the point where it is all you need, and one can just discard philosophical thinking?)