Explain why it is better and define why it is misleading? I am curious about this viewpoint difference.
Let us suppose a person is looking for a specific function about Player scripting, doesn't know exactly the name neither knows what the function does. He/she is obviously trying to look for a general/catagory section called "Player scripts/codes".
1) According to you and Sparen, we should link them to the entire list of functions. The reader will be summoned a huge page with all the functions of Ph3. No problem you might say as a quick search for 'player' will be pointing him to the right section. The reader discovers he/she was looking for 'IsPermitPlayerShot'. Clicks on the link and ends up at http://dmf.shrinemaiden.org/wiki/Player_Functions#IsPermitPlayerShot
2) According to the current situation, the reader is summoned an overview of all catagories of functions. Let us say the player remains point of interest. The reader looks at P and noticed Player Functions and clicks it ending up on the same link.
Both situations are valid and useful, except the latter gives in my opinion a pleasant overview for the eye and look up. We shouldn't forget that people who are unsure about a certain name of a function, should be given a helping hand to look under a category. Both styles do this, but the latter is has a better structure and more overview. I remember 0.12m on touhouwiki was put roughly like this which is why I kept this style currently.
1) It's misleading because the "functions" category page actually just includes all ph3 pages, not just functions. I don't have an objection to a category page for ph3 stuff, but at least label it properly.
2) You can't search for individual function names on the category page, but you can search for function categories on the full function list. Therefore, the latter offers more functionality.
Example: You gave the example with IsPermitPlayerShot where it might be slightly easier for a novice to find, but consider this... Say you want to know about the function GetPlayerRenderPriorityI. On the full function list, you can find it easily even though it's actually a System function. On the category page, it's easy to make the mistake of looking through ObjRender functions, ObjPlayer functions, Player script functions, etc. This can easily happen to both novices who don't know the exact name, and experts who do.
Perhaps a link to the category at the top of the functions page would be better, so that if the reader cannot find what he's looking for in the functions page (like possibly the list of default bullet graphics), they can search all pages in the specific danmakufu version.
Things like that should be placed under a different category of ph3 documentation, along with default render priorities, event types, and other things that aren't functions. They would be on the category page for ph3, and for this new type of miscellaneous documentation, but not on the function category page as they currently are.