No, I'm not asking if "dot operator can throw a NRE" is a mistake; I'm asking if the dot operator, the ability to access members at all, is a mistake.

One take on it is that yes, the single dot operator was an ancient mistake which is why so many programming language features are about making it smarter. Properties as mentioned in this article are an ancient way to fake the dot operator into a "field" but actually make method calls. Modern C# also picked up the question dot operator (?.) for safer null traversal and the exclamation dot operator (!. aka the "damnit operator" or "I think I know what I'm doing operator") for even less safe null traversal.