Do users really need to search through a tag page?

My video site offers full search functionality that searches based on title, description and tags.

I also have a category page that has 20+ categories to browse (each video is categorized as well as tagged).

I want to make a tag page that lists all the tags and the amount of videos that share that tag. This will help users who want to browse popular tags who wouldn't have known what to search.

I'm debating whether or not on this tag page to add a search within the page that allows users to filter through the list of tags. Similar to ux.stackexchange.com/tags. My site will have ~5k tags.

My first thoughts are if people KNEW what tags to search for they would just type them in the search box so having a search on the tag page itself is useless, right?