What is the use of singletonList?

It works like a charm:

List<String> list = new ArrayList<String>();
list.add("abc");
list.add(null);
list.add("def");
list.removeAll(Collections.singletonList(null));
System.out.println(list);  //[abc, def]

Indeed Collections.singletonList(null) is immutable (which is unfortunately hidden in Java^[1]), but the exception is thrown from your list variable. Apparently it is immutable as well, like in example below:

List<String> list = Arrays.asList("abc", null, "def");
list.removeAll(Collections.singletonList(null));

This code will throw an UnsupportedOperationException. So as you can see singletonList() is useful in this case. Use it when client code expects a read-only list (it won't modify it) but you only want to pass one element in it. singletonList() is (thread-)safe (due to immutability), fast and compact.

^[1] E.g. in scala there is a separete hierarchy for mutable and immutable collections and API can choose whether it accept this or the other (or both, as they have common base interfaces)

To answer your actual question :

what would be a typical use of this singletonList? To represent a collection of size 1 when you're sure you don't want to actually do anything with the collection?

The typical use is if you have one element and want to pass it to a method that accepts a List, ie

public void registerUsers(List<User> users) {...}

User currentUser = Login Manager.getCurrentUser();
registerUsers(Collections.singletonList(currentUser));

The removeAll() is a special case for this.