Searchable Categories allows a quick real-time search through categories while selecting in new post/edit post view.
Just what I was looking for!
There is a field to search / filter categories in the categories metabox for menus.
I don't understand why this feature is not available for posts.
It should definitely be included in WordPress by default.
Fortunatly I found this plugin!
I had put 5 stars but I removed one.
I noticed that with this plugin, the selected categories are no more displayed on top of the list. So, you must scroll down to know what categories are selected… not very convenient!
It would be perfect if this could be fixed.