A test server would take the excitement out of new content patches, as well as it would let people prepare for different parts of the content. Unless they change the content right after it was on the test server to prevent that kind of issue, this would not be a great outcome.
Another aspect would be the limitation of people that can join the test server, SE is not gonna put up a whole server, in different regions, that 2+ mil people can join at any time. It's difficult to determinate what kind of players can test the upcoming content and who doesn't. There would be always people that feel left out because they weren't able to join the test run, as well as people that would complain about changes being made at the end/start of each test run.
Also the game is not in beta stage anymore, that's the whole point of test servers when it comes of including the public. We did have closed and open beta's around 4 or 5 years ago. Sure we all know that the community changes, however the gaming mentality does not. SE decided a long time ago, who they like to cater too, some might like it and others won't, but at the end of the day that's SE's decision. I am not going to decide for them what content is plain out tedious and what content would be great if specific changes are made. They decided on this kind of business model, now they need to figure out how to make it work.
Was I disappointed about the patch? Yes but this was the only patch I wasn't happy with and that's my own problem. Lots of people enjoy the content that has been added a day ago, and that's the majority of people playing the game, or at least the majority of people voicing their opinion via forums. Only source SE can gather information from and there's nothing wrong with that. A test server would have not changed that.
So back to topic, with all this mentioned above and a couple of other things that need to be taken in consideration, at the end it would be the wrong move on SE's end. It would look very desperate and unprofessional, just to please a couple of unhappy customers.
Should SE care about their customers? Yes definitely, however you need to take into consideration how much of those complains are the truth. Some people just complain for the sake of complaining, others blow it out of proportion and then you have just a few, that might not like something but can't give non bias criticism or make any suggestions of how things could be changed. You can also not forget the silent player base, that does play a huge factor when it comes to the statistical part that dev's are looking at.
There's so many things you need to take into consideration, just opening a server is not that easy as it might seem like and absolutely not necessary.