Personally, I'd rather be able to click "move" on the category page and have it do it automagically. Why do we have to add another special page for this?

A few things:

• it should also allow to merge several categories into another one : [[Category:Foo 1]], [[Category:Foo 2]], etc, into [[Category:Bar]]
• it should allow to depopulate a category (in view of its deletion), so the bot would just remove [[Category:Foo]]
• the special page should be restricted to users with the appropriate userright, it may be limited to categories of a certain size, and another userright with a higher size limit or no restriction may be given to admins

Personally, I'd rather be able to click "move" on the category page and have it do it automagically. Why do we have to add another special page for this?

In order to handle the cases of multiple categories to merge into another one (which may already exist on its own). It happens quite regularly at Categories for discussion (there are sometimes a dozen or more categories to merge). Plus users often make mistakes on the target name when moving pages, a confirmation step would be appreciable before the bot starts editing hundreds of pages. A handy link to the special page may be given after a category page move. If desired, a user script that prompts the user to use the special page indirectly when moving a category page may be made.

Personally, I'd rather be able to click "move" on the category page and have it do it automagically. Why do we have to add another special page for this?

In order to handle the cases of multiple categories to merge into another one (which may already exist on its own). It happens quite regularly at Categories for discussion (there are sometimes a dozen or more categories to merge). Plus users often make mistakes on the target name when moving pages, a confirmation step would be appreciable before the bot starts editing hundreds of pages. A handy link to the special page may be given after a category page move. If desired, a user script that prompts the user to use the special page indirectly when moving a category page may be made.

That sounds like an entirely separate task of creating a new Extension:MergeCategories and I wouldn't oppose that if it was in its own ticket. The purpose of this ticket however is to make Special:Move properly move categories and not merge them.

It would work in pretty much the same way in terms of implementation and coding so an extension should be built to handle all of those cases, rather than each separately. When that is done, it can be customized to each specific use.