Why does a static constructor not have any parameters?

Because you can't call it directly (as per MSDN):

A static constructor cannot be called directly.

Static constructors are called automatically as part of type initialization. They're not called explicitly... so there's nowhere you could provide any arguments to correspond to the constructor parameters. Why would you want to allow parameters if you could never specify any values for the arguments?

How would you control the arguments that were passed to such a constructor, given that it's invoked automatically by the run-time when the class is referenced for the first time, and can't be called directly?

In theory, such a syntax could have been devised and implemented, but then that would necessitate its direct invocation, since now a simple class reference won't know what to pass in as arguments to it. The whole point of the static constructor is to perform type-level initializing prior to using the type. Doing so automatically ensures that this is the case, whereas direct invocation leaves plenty of room for mistakes.

As MSDN says, A static constructor is called automatically to initialize the class before the first instance is created. Therefore you can't send it any parameters.

If the CLR must call a static constructor how will it know which parameters to pass it?