I am enrolled at a small graduate program in the US. I came here because the PhD advisor I will be working with has a great reputation and because I wanted to work with her. However, the courses I am taking here are simply not up to the mark from what I expected good graduate courses to be. I am worried that if I start my PhD without having good courses I will be under-prepared to handle challenging problems later, and my exposure to interesting physics would be limited the ones I encounter during my research. People who are past their PhD programs, how important do you think coursework is? Do you think it is worthwhile transferring to another PhD program now?
I am worried that if I start my PhD without having good courses I will be under-prepared to handle challenging problems later, and [various bad things]
There are a few things to note here that might put you at ease. Firstly, while it is true that the quality of the material and instruction in a course certainly matters, even more important is the drive and work ethic of the student. Depending on your willingness to engage deeply with the material, and search out other material, you can pretty much make your course as rigorous as you want it to be. If you find that there is a gap in the material in some respect (e.g., some mathematical assertion that is not proved and that you don't know), look up other material to supplement what is in the scope of the course. Since you are a PhD student now, one of the things you should be getting good at (or at least practicing with a view to getting good at it later) is looking up other sources of material to supplement gaps in knowledge.
Beyond taking courses as a student, a very effective way of learning a topic is to teach it. Since you are a PhD student, you should have some opportunities to tutor some of the early undergraduate courses in your field, and maybe even some of the later undergraduate courses. If you become an academic, you will probably end up teaching both undergraduate and postgraduate courses. Teaching a course requires you to fill out a deep and systematic knowledge of the subject that goes well beyond what was required of you as a student (even as a high-performing student), so it is a very effective way to solidify your knowledge. Obviously right now you will not be teaching your graduate courses --- you are the student here. But you can look for opportunities to teach into some early undergraduate courses, which will get you on the path to solidifying your knowledge of foundational material at a deeper level.
Finally, don't make the error of thinking that your learning ends when your coursework ends. Even after you have finished all your courses and you are doing pure research, you will find yourself exposed to thorny problems that necessitate learning new material, or going back and relearning material you have previously studied and forgotten. Often a formal course undertaken in graduate school is just the first iteration of learning a topic --- you do the course and learn a bunch of things, and then if you don't apply them for a long time (e.g., years or decades) you forget a whole bunch of it, and then when you need that material you relearn it, and so on. The main advantage of doing the formal coursework in your training is that when you find you need to relearn it later on, it is a lot faster.
The main purposes of coursework in a doctoral program in the US is twofold.
First, they give you some breadth of field and assure the faculty that you have broad knowledge. For this purpose it may not matter so much that they are less rigorous than you would like. People in the US, anyway, feel that PhDs need a broad view of their field to serve as a basis.
But the second, more important purpose, for the candidate, is that they prepare you to get through the (usually) necessary qualifying exams, sometimes called prelims. The faculty has probably tailored the coursework at that level.
Some programs actually only have two requirements: Pass qualifiers and write an acceptable thesis. In that case, the coursework may be irrelevant for some students if their training is otherwise sufficient.
But after you finish a degree, few people will be concerned in anyway with your coursework. An exception might be in a teaching institution, where the department head might want to know that you will do a good job teaching certain necessary subjects.
I would talk to your supervisor about this. She is probably as ambitious as you are if she is as good as you say, and it benefits both of you for you to be well prepared for the work.
It is an unfortunate fact of life that sometimes you have to waste time jumping through hoops to get where you want to go, but if you are in courses any way, there should be some way you, the instructor, and your advisor can come up with to make sure you get the knowledge and training you need out of the experience. If not, you can also self-teach, arrange to spend a semester at another school and take their courses, arrange to teach the course yourself (then you will really learn the material!) or take a summer school course on the material.
Finally, it is possible that your expectations for postgraduate training are too high---quite often postgraduates are expected to work out a lot more things for themselves than undergraduates. Your supervisor is way more likely to be able to assess if this is your problem than I am or anyone else not at your university is, so I would talk to her first and foremost.