I wonder if and how writing \"almighty\" classes in c++ actually impacts performance.
If I have for example, a class Point, with only uint x
You have already got some pretty good technical advice. I want to throw in something non-technical: As the STL showed us all, doing it all in member functions might not be the best way to do this. Rather than piling up arguments, I refer to Scott Meyers' class article on the subject: How Non-Member Functions Improve Encapsulation.
Although technically there should be no problem, you still might want to review your design from a design POV.