Music Ed for teaching in the public schools. Instrumental or vocal. With piano, you would probably be put in the vocal/general music category -- That means teaching kids in a classroom. K-6. There is also junior and high school general music class too. This is of course not much like private piano lessons -- content or skill-wise.
I can see a music ed degree being very useful for someone interested in teaching more of a "piano class" "movement class" "introduction to music" type of class. The classes for young kids. If you have a general music background (and Orff, Kodaly, etc.) that could help out that kind of teaching.
Talk to a counselor at a university or college. No offense, but I don't quite understand why the let you in if you don't want to do music ed. Talk to someone there who can explain this in person.
Yeah, 100% job placement rate. What they don't tell you is the type of job you get -- probably garbage, the ones that other teacher don't want, a starter job where things are far from perfect. What else don't they tell you? 50% of teachers quit after the first year; 70% within the first five years. So, you get the job, but do you stay and can you keep it? Either way, the college has already made its money. I can't imagine the dropout rate during college. That must be huge -- maybe 10% actually making it all the way through?
The piano performance degree. You may need more than this. A masters at least -- in performance. The dual piano perf and piano pedagogy idea is good and doable. A performance degree means squat though. It's how you play that will get a gig. No one cares if you have a degree and if you are playing somewhere they will probably just assume it -- Of course, they have studied and went to school.
With the performance degree, you have a big "so what?" waiting after you graduate. With the ed degree, you have the entire public school system there. Both have pros and cons. If you plan on running a private teaching studio, business classes are not a bad idea either. A business minor is always an option, but you can't neglect your development if you do performance. Building a teaching studio and reptution takes time.
You have to decide what to do of course. The ed degree is much more stable but you become part of a system. The private teaching studio is less stable, but you have more control.
I think a lot of private (MTNA wants people to use the term "independent") teachers make their living by teaching, performing, and maybe some other part time job to make ends meet. Or they survie with financial assistance from their spouse.
Maybe you can find some people who are already working in these fields? Meet them, see if they are doing something you would like to do. The college advisor is going to give advice, but they also work for that college ($), and they will give you a degree if you do all the work and pay for it. That doesn't mean that degree with enable or guarantee that you can get a job with it.
If you're running a private studio, survival depends on many things -- like location, an area that has the interest to even support a private music teacher.
The theory degrees. I think those are for the people who want to go on to become theory teachers -- at the college level. But teaching at the college level usually means a doctorate. So if you got a theory bachelors, probably a theory masters and then doc would follow. I'm kind of out of my element in this area though. Same with music history.
Good luck. Kind of sucks to have the real world creep in like that though.