I have to assume that some people at least tried.
For your initial examples, there simply isn't any canon information to help us. I am quite certain that there would be a huge political backlash which would attract attention, and the families of the trapped players would also be seeking out help. However the entire story was told from the point of the players, and there was no announcement that anyone made it out alive otherwise. That means details of various failed experiments simply added to the near 4k dead by the end of the experiment.
However I believe that it was entirely possible to release all of the players, but then a very delusional man named Sugou came along.
The biggest thing that I want to stress is that the brain-frying function of the NerveGear was understood very little. While it was explained to everyone within SAO, we have no idea how much information was given on the outside.
Except we know that the company who developed SAO, Argus, went bankrupt due to the SAO incident. Their assets were acquired by RECT Progress Inc., who formed a Fulldive division headed by Sugou to overlook the SAO servers and assets including the Cardinal System. Furthermore, we can tell that they have the direct source code to the system based off the modifications that they have been able to make. This includes upgrading the system to improve on things that it couldn't do before, and also modifying the Logout function to redirect 300 users to their own server.
Here we're dealing with a team of people that has access to the full server software, the hardware that it runs on, and the connection that goes out from it. On top of that, this team has full documentation on the NerveGear (they did co-develop the NerveGear's successor), and they have shown to be able to modify the existing SAO game. This means that this team, with time and patience, could have done any of the following:
- Restore the logout button
- Forcibly log everyone out
- Modify the "death" script to no longer instruct the NerveGear to fry the brain
- Disable the NerveGear remotely
However this didn't happen. Instead, 300 unlucky people were transferred from the hands of one madman to another.
Now remember that this one small division of people were responsible for the lives of many thousands of people, and they had nefarious plans. It was in their interest to keep the players inside the game in order to avoid any attention to their true goals. They were so good about keeping secrets that they were able to design an entire game world around the very place they did the experiments in, and not one person in the company found out. Remember that this was such a commercial success that Sugou was to inherit the company, however nobody else in the company figured out what was going on.
What's even worse about this secrecy is that this treasure-trove of information is kept from the public. The "experts" in the field are the exact same people who want to keep everybody in the game. Now if you wanted to free your relative from a death game, would you put your trust in Joe Schmoe who has a theory but no solid evidence? Or would you trust the kind team of dedicated individuals who are experts in this area and tell you that nothing can be done?