Hmmm... I'm willing to be pushed by my teacher, but I don't want to be made to break down and cry! I don't think it'd make me better at piano, maybe the opposite.
I don't think teachers who make their students break down and cry necessarily produce students of a very high level. But that is just me... I think different teachers suit different personalities. I'm quite sensitive.
I think that if I ended up crying every lesson, it would probably take an emotional toll on me, and whatever caused me to cry would be in my head the whole week whenever I go near a piano--- which is not productive...
I also think I would not be able to be myself when playing in front of my teacher, for fear of being yelled at.
I've never had an extremely strict teacher before though (I have had a teacher who yelled at me, but she did not make me cry, and I'm sure there are much stricter teachers out there), nor do I consider myself a student of a very high level.
However I can say that my teacher pushes me to want to play better. She doesn't sugarcoat anything when giving constructive criticism. Sometimes we laugh at my mistakes, but that makes me remember what I did wrong and doesn't make me the least bit upset. She takes me seriously and understands that I don't just want to play piano, I want to play well. I've told her my goals, and using my goals my teacher's created a plan for me, and told me what
her expectations are as well. My parents have told me that if I take piano seriously, my teacher would take me seriously. When I challenge myself, it is in a way challenging the teacher, and she will push and challenge me in return. I think that is probably true... it's a two way thing. I don't know if I'm working harder now because my teacher's pushing me harder, or if she's pushing me harder because I'm working harder. I think it's both.
Maybe you could ask your friends for recommendations. But my points are: 1) teachers probably will push you more if you push yourself and 2) good teacher doesn't necessarily mean one who makes students cry!
Disclaimer: I'm not one of those "students of a high level"

(but I try my best!)