The following are the only ways classes are different from structs in C# (please correct me if I\'m wrong):
Reed's answer is quite good but just to add a few extra points:
please correct me if I'm wrong
You are basically on the right track here. You've made the common error of confusing variables with values. Variables are storage locations; values are stored in variables. And you are flirting with the commonly-stated myth that "value types go on the stack"; rather, variables go on either short-term or long-term storage, because variables are storage locations. Whether a variable goes on short or long term storage depends on its known lifetime, not its type.
But all of that is not particularly relevant to your question, which boils down to asking for a refutation of this syllogism:
We can refute the syllogism in several ways.
First, yes, mutable structs are evil. However, they are sometimes very useful because in some limited scenarios, you can get a performance advantage. I do not recommend this approach unless other reasonable avenues have been exhausted and there is a real performance problem.
Second, reference copying is not necessarily cheaper than struct copying. References are typically implemented as 4 or 8 byte managed pointers (though that is an implementation detail; they could be implemented as opaque handles). Copying a reference-sized struct is neither cheaper nor more expensive than copying a reference-sized reference.
Third, even if reference copying is cheaper than struct copying, references must be dereferenced in order to get at their fields. Dereferencing is not zero cost! Not only does it take machine cycles to dereference a reference, doing so might mess up the processor cache, and that can make future dereferences far more expensive!
Fourth, even if reference copying is cheaper than struct copying, who cares? If that is not the bottleneck that is producing an unacceptable performance cost then which one is faster is completely irrelevant.
Fifth, references are far, far more expensive in memory space than structs are.
Sixth, references add expense because the network of references must be periodically traced by the garbage collector; "blittable" structs may be ignored by the garbage collector entirely. Garbage collection is a large expense.
Seventh, immutable value types cannot be null, unlike reference types. You know that every value is a good value. And as Reed pointed out, in order to get a good value of a reference type you have to run both an allocator and a constructor. That's not cheap.
Eighth, value types represent values, and programs are often about the manipulation of values. It makes sense to "bake in" the metaphors of both "value" and "reference" in a language, regardless of which is "cheaper".