Well I do like your thinking, and do agree with it. However, that can't say she might not be crazy.
Insanity is not something you are born with. True others might be more susceptible to it than others, but it still is something that is only created. Insanity, and being crazy is all due to having to much/to little of a chemical in your brain, and that is caused by having to much trauma in the past of your life. You are right when you say she would be depressed. Most insane people have been depressed, which is what comes with trauma. School shootings are usually cause of the student being bullied to much, and having nobody there to stand up for them. That person will feel that there is nobody there who cares about them, and everyone is against them, putting them thru so much pain that they will get to the point where they feel the only way to get rid of it, is to kill everyone. Most people who commit crimes are looking for that attention that they were never given. Usually people who fought in a war, had an uncaring family, or lost a lot are as well in chance of becoming insane, due to the trauma.
Pinkie lived on a rock farm. I think even if she makes it seem like it was great, she's hiding in the true fact that she was totally miserable there. Until she actually threw a party, her family didn't seem like they ever smiled. Perhaps they didn't show her enough love. She needed love, and for someone to be around her when her family wasn't so she freaked out when her friends didn't show up to gummies party. I personally believe that pinkie had to have had a harmful past, therefore creating the monster of pinkamena. Almost as if someone who has DID.
This isn't just stuff I make up. I have been studding the brain almost all my life, and I actually do have DID due to my past, so it really is something that can ruin a happy fun pony, and turn them into a killing monster. You have to be careful with how you treat those around you, because even if you don't notice, every thing you do, they take note of it.