We often use student ID (currently implemented as our usernames) as a method for searching for and finding a particular student.
This is a great suggestion, but not one we have the resources to tackle right now. However, I have added it as item 6 for the v13 todo list.
I can’t offer a custom search in Fast Finder just yet, but your particular request for Student ID search in Fast Finder has been met by @skuipers in v13. Yeah!