Your compiler giving you a type check error is saying that the program is meaningless. What is the advantage of running a program that is known to be wrong?
The design of the type system will define what is meaningful/meaningless per type check rule (eg a missing branch which can be a warning vs an ambiguous type inference that means the program cannot be compiled). The question is really whether you want to design a type system that can be checked statically, which to me the no-brainer answer is "yes."
I don't want to have to run the program to know if it type checks. I don't want to have to run it to know what types are in the program, or the signature of functions. I want my tool to tell me when my code is provably wrong, and to prevent provably wrong code from being merged into a codebase without executing it.