Why is the clause "who was wearing a blue hat" in the first sentence(1) a defining one? It seems to me to me that this sentence is clear in its meaning if we omit this information and regard this sentence as a sentence containing a non-defining relative clause and separate "who was wearing a blue hat" with commas(2).
(1)A woman who was wearing a blue hat opened the door.
(2)A woman,who was wearing a blue hat,opened the door.
Thanks in advance.