They are what make the theory look sillier the more successful it becomes. The problems are listed in Appendix . Beyond this intuition is able to consider possibilities that intellect cannot deal with. Intuition is always ready to start over. For intellect to proceed in physics it must have or work out the the mathematics in some detail.
Intuition can play with ideas at a looser level.
Intuition can leave the conceptual framework of classical particles that is trapped in. Without knowing the details it can match patterns and see where connections are possible in a different framework. Of course this process is far more error prone then a more narrow intellectual approach, but for many problems it is the only possible approach. It is the starting point that must precede an intellectual solution.