I have a policy of “accept all friends” and I have 500 friends in my friend list.
For users with many friends, it’s very hard to find a desired person in the friend list - and at best involves a lot of meticulous scrolling, at worst - large numbers of friends overload the friend list UI and it doesn’t load fully/correctly.
Having a text input to filter this list to find a particular friend would be a great user experience improvement.