Should I apply to PhDs in the US (theoretical physics)? I am a Cambridge Mathematics undergraduate (third year) and I want to be a theoretical physicist (I am taking the relevant courses, research experience, etc). I am confident I can get into Part III, but not sure if I could get accepted into an Oxbridge PhD. I would start my PhD in October 2021, so if I want to go to the States I should start thinking about GREs soon.

Should I consider applying to US top schools? 
The application process would we quite time-consuming, but I am not sure I would end up going to the US over other European universities. Some points I am considering about grad school in the States are:


Longer (5-6 yrs) PhDs compared to Europe (3-4 yrs), it seems better to save 2 years. (Although I am young, so it may be good to have some stability before postdocs)
Coursework required may overlap with my Part III
Expensive (?)
If I do not get into an Oxbridge PhD, then I probably would not get into a top US school either. In that case, I think I would prefer a second-class European university than a second-class US university. And if get into Oxbridge, I would be more than happy to stay. Hence, with this reasoning, either way, I should not bother about applying to the US.


I think it is relevant to note that I would be 21 at the start of the PhD.

EDIT:
To clarify, my main question is not what are my chances of getting in, rather if it is worth doing a (longer) PhD in the US instead of somewhere in Europe (probably not Oxbridge).
I think that the only issue here is that you intend to change fields. You will need to show a US institution that you have adequate background in needed physics topics to begin advanced study. But you may be fine there also, depending on your course of study. 

The reason that the US degree takes longer is that it makes fewer assumptions about the candidate's background on entry. A doctoral program (here) normally requires some advanced coursework leading to comprehensive (qualifying) examinations. So, there is some opportunity to make up for missed subjects, provided that you can convince a department to take you. Letters of recommendation might be essential, especially if they can speak to your readiness to switch fields. 

And, you might be able to get into a top program (depending), since the entrance requirements are a bit less than for Oxbridge, which has a different educational system. In particular, an undergraduate degree in UK is normally more specialized than one in US, whereas most students here can enter doctoral programs with only that less specialized undergraduate degree. 



Following your edits, I can only add that the decision about whether it is "worth it" is personal and can only be answered given your own preferences. Weigh the plus and minus aspects of each decision as you would for any important one. You are unlikely to suffer any major setback to your career no matter which way you jump.