Move and patrol is useful
before the castle is under siege, not after. It was never (to my knowledge) used for entering the castle. The whole point of move and patrol is to allow reinforcements to assist province defense and/or units that are already in the province with patrol orders.
To word it another way, move and patrol to protect the province before it is attacked. When the castle is under siege, the province has already been lost and any units moving into the province will attack the sieging army.
(Sorry if that is not clear. It is 3:23 am here and I should have been in bed hours ago.
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