>Oracle supports ORDER BY in views and has for several versions. Is there any reason why I should not use it?

What benefits do you get by using views with ORDER BY clause?

It's not a part of ANSI SQL standard and may not be available in other databases.
Also a query w/o ORDER BY clause is not suppose to return records in any particular order. IOW, if you switch FROM from a view to a table you'll get different result which is inconsistent.