File System falls in the “cookies and other site data” setting, which means clearing it will be a problem, because if you downloaded files from a website, like Mega, which is the only site I know that uses File System so I use it as an example, and you had an account and all that, you will lose the login information, because you cleared the cookies as well.
File System is just another type of storage, and the problem about it is how it grows but never gets stopped by the browser or cleared or anything.
In the case of Mega, when you click the download button, the file gets downloaded to the File System, then when it finished, it asks the user where you want to download the file, but all it does is copy the file from File system to the selected folder, the only difference is one will be stored as 00000000 and when you tell mega where you want to download the file, it will have proper name and extension. but Hash matches and all, so you can just copy the file from File System, change the name and extension and it will be the exact same thing.
That’s why deleting the File System folder won’t do anything different of what Brave/Chromium does it when you clear it, when you clear it through the browser, the File System/Origins folder stays in the user data, that’s all. the only ones that get removed by the browser are the ones with numbers 000, 001, etc.
Of course, Nightly recently re-added the way to see Storages in Brave which was removed by Chromium, it is located in brave://settings/cookies/detail?site=mega.nz for example, and just clearing there is the easiest way. But who knows when Stable is going to get it.