Generally most of them are patient and helpful. In the end though, metrics on the tickets they work factor into their performance reviews.
So they are trying to keep ticket volume up, time to resolve/close on a ticket low.
Then there is a factor of which call center took your ticket. I'd rate the people in Cork Ireland and Austin at the top. The folks in the Philippines at the bottom.
Regarding closing the ticket without the customers knowledge...bad form. I understand sometimes getting a customer to respond can be frustrating. If there
is a documented attempt to contact the customer with no response after several attempts then I can see a case for closing it. If it is a, "oh...its working now, closing the ticket", then
maybe not.