What makes you think people didn't long toss before 1980? It is just a name for something that has been done almost since the invention of baseball.
The reason for the more recent implementation of long toss is that done on an arc, gradually increasing distance, it has been used for rehab. When it is done that way it is a bit safer. It still isn't perfectly safe. Almost no throwing is completely safe.
Long toss isn't a miracle. It helps some. It doesn't help others. Some pitchers benefit more from bullpens and flatgrounds. There's only so much time/(wear and tear)/catchers available and each player has to determine what mix works best within those constraints. Each player has to find out what works for them and what their body can and can't handle. Parents need to help with that a bit until the players are ready to take over for themselves.