I am sorry that you had such a poor experience in the application process. However, I hope that you are not too discouraged as it sounds like you have a strong profile since you received interest from some top schools. Remember, these PhD programs are highly competitive and it only take two or three people who have a better day on the interview for it to make a difference between an acceptance or a rejection.
It definitely sounds like you have the drive to be a good academic.
Bocconi is a great placement and a PhD from there will set you up well for the job market. I would say that they are easily on par with top 30-50 programs and could also possibly help you crack top placements if you have a stellar publication record. So I would think hard about going there if you feel that you can make it work.
It sounds to me like your motivations for getting a PhD are not research driven which likely set off red flags for a lot of the top schools you applied to. They care a lot more about research and may have passed over your application in favor of someone who was more research focused. Your interest in teaching is not bad and I think a good number of people who get PhDs are initially motivated by teaching interests. However, if you choose to go through another application cycle, I would suggest emphasizing research interests rather than teaching interests. If you feel like research is not something that you would enjoy (and I mean really enjoy to the point that you are happy doing it 40-60 hours a week throughout the PhD program), then I would also recommend shooting for lower ranking R1s that will create less of a research-centric "pressure cooker" environment. Any R1 PhD program will still be research intensive but some are more ok with students placing in balanced or teaching positions.