There are costs, and they go up significantly the more sophisticated your type system is/the more speicifc you try to be with your types.
The way I see it there are two kinds of costs type systems may impose. Very simplistic type systems, such as the ones in C, Go, and even C++, Java, C#, often force you to write code that is too specific, thus forcing duplication (C and Go especially suffer terribly from not having generics - in Go especially its impossible to write a well typed function that can be passed an array of any kind and return an element of that array).
On the other hand, of your type system is powerful enough, you still get a similar problem when trying to write code that is abstract enough to be reusable, but specific enough to be safe.
For example, if you were writing code for a physical simulation system, you would want to have all quantities carry their measurement unit in their type, to avoid mismatches.
However, you wouldn't want to rewrite maths code for each measurement unit. However, to properly keep track of types in complex maths code gets pretty ugly pretty quickly. For example, a function that wants to compute the scalar product of 2 2-dimensional vectors would only work if the first values of each vector have the same/convertible units as the second pair, in any order (m,s dot s,m should be ok). If you move to matrix multiplication, the types become even more complicated, and this is still very basic algebra. If you want your function to be applicable to arbitrary matrix sizes you're already writing a complex library.