create or replace function next_day_start (
  p_date in date
) return date
  authid definer
is
  l_date date not null:=p_date;
begin
  return 1 + trunc(l_date);
end;

You're getting this because the only thing you do after assigning a value to the variable is return it. i.e. you don't make any further changes to its value.

As the docs say:

Cause: This assignment may be unnecessary; the PL/SQL optimizer could not find any further use of the variable which was being set. If the assignment was being done for some side-effect such as raising a specific exception, the compiler may not have been able to understand the side-effect and this warning may be inappropriate.

Action: If the assignment sets a variable whose value will not be used again and there are no side-effects (exceptions or calls) to consider, remove the assignment for better performance. If the assignment was in place to raise a specific known exception, replace the assignment with a RAISE statement.

This is one of the instances where it's unable to detect a side-effect. Notably that the code raises an exception if the parameter is null.

If the warning is annoying you, there is a way around it.

PL/SQL parameters inherit not null constraints from their types. So you can declare a subtype as not null. And use that in your parameter definition:

create or replace package pkg as
  subtype date_nn is date not null;
end;
/

create or replace function next_day_start (
  p_date in pkg.date_nn
) return date
  authid definer
is
begin
  return 1 + trunc(p_date);
end;
/

select next_day_start(null) from dual;

SQL Error: ORA-06553: PLS-567: cannot pass NULL to a NOT NULL constrained formal parameter