Thanks for sharing your concerns. Regardless of how you came to came to join the Navy's nuclear power program, I can understand your doubts about your future.
The thing that strikes me is your own admission that you do not have a clear direction as to your career. That happens to many people, as you mentioned. When I joined the Navy, I had just become a senior with majors in Chemistry and English, but I had stopped going to school full time and was working at a campus security job while taking courses in Sociology. That sounds exactly as you described having heard. Even after taking classes in different fields, I still did not see how a college education would apply to a career.
The problem is that you are looking at the Navy as a possible waste of time equivalent to that of an aimless college program. You mentioned that you were attracted to the Navy because of the "free college tuition". The educational opportunities in the Navy do not begin once you have fulfilled your six year commitment. You can take college classes while in the Navy, paid for by a program (the Tuition Assistance program) that does not reduce the college benefits available to you through the GI Bill. I, myself, used tuition assistance to pay for Certificate program courses in computer programming and hazardous waste management, Russian language courses, physics, psychology, political science, history, and other general education courses. You can explore various fields until you know what will be your field of interest for a college degree.
Before I go on, there are, of course, a few clarifications. Your primary educational objective is toward your Naval career, and your nuclear power studies come first. You will have to devote much of your time for the first couple of years learning how to operate nuclear plants, in general, and then to make yourself useful when you get stationed on a ship. But the good thing is that those studies can be evaluated for college credit. (I am not going to go into detail about how much, because there are whole threads in this forum on that subject.) But the most important thing, I believe, is that you are getting work experience that employers will look at and consider valuable. Imagine going for an employment interview, assuming that you have done your six years in the Navy and completed the college degree of your choice, and being able to say that in addition to your degree, you have six years work experience, including management positions. Compare that with someone who has wandered from degree to degree, working at fast food restaurants and other part time jobs. Who would you rather hire?
You can read in other forums how achievable it is to get your college degree while still in the Navy. I must say that I did not find it as easy as other people make it sound, in spite of all the courses I was able to take, but when I was in the Navy, everything had to be done by mail, and now with the internet and CD-ROMS, video tapes, and the like, it is much easier these days.
Ok, enough of that approach. Yes, I was a Navy recruiter, and one of those recruiters who went around to high schools (although I talked mostly about how nuclear power works rather than Navy benefits). I mentioned that because I like everything to be out in the open. But also, I am speaking from personal experience, as someone who was undecided about a career, as you said you are.
Obviously, as evidenced by your test scores, you're intelligent and have a high aptitude for subjects related to nuclear power. I'm addressing your concern that you don't like physics. I didn't care much for physics, even though my major was chemistry. So, I don't really know much about how physics in high school is taught these days or what you know about Nuclear Engineering. All I can say is that with your aptitude, if you apply yourself, there's no question that you'll be able to succeed in the training. I can't really say much about Nuclear Power training, since I went through the program 20 years ago and things may have changed, but Navy training isn't like high school. It's fast paced, with definite objectives, and little or no wasted time. For the most part, there is a hands on component, but you aren't doing "experiments" like in a high school or college class. I doubt that you'd spend much time asleep in class. As for failing tests ... well, it's your career development, not just passing a class.
For a person looking for direction in life, the Navy can be a valuable experience. Sure, people are telling you what to do, but for some people, isn't that what you're really looking for until you gain your sense of purpose? It's a well paying, full time job (and when I joined, before President Reagan normalized military pay, it was a good occupation even before the pay hikes and all the things like enlistment bonuses that are offered now). Your six or more years in the Navy are whatever you make them. You can even be the stereotypical sailor, and then, yes, you will have wasted your time when you get out at age 26, but if you continue with the nuclear power program, it won't be because the opportunities weren't there for you.
So maybe the opportunity you have has been presented to you this way and perhaps not. If you want to know more, there is certainly lots of good and bad you can read about in these forums. I can't say that my entire Navy experience has been positive. In particular, I never wanted to be a recruiter. Sometimes you just have to know when to get out of the Navy, too. As undecided as you might be right now regarding your career, if you do go into the Navy's nuclear power program, know right now that you will make the most of your time in the Navy if you can set some clear goals for yourself. If that college education is important to you, make sure you know how much Tuition Assistance is available to you each year and make sure you use it to its fullest extent. It might give you the incentive to excel at your Navy schools to give yourself the opportunity for an instructor position immediately following nuclear power training, which would give you the opportunity to take advantage of the programs that some colleges at or nearby the Navy facilities.
Anyway, the Navy can be more than just a free ride for college tuition. But as a former recuiter and fleet sailor, the last thing I want serving beside me is a person who really doesn't want to be there. I don't want someone who feels that he or she wasn't told the complete story and was misled about this or that. But as you said, once you make a decision, there's no turning back, so whatever you do, be informed and be realistic, don't compromise, and make the most of your opportunities.
Best wishes with your decision.