Why does Interlocked.Exchange not support Boolean type?

Yes, there is a good reason. The implementation of the Interlocked methods requires low-level support at the processor level. See this answer for example. That's an issue when you define a framework that's architecture agnostic.

Implementing the low-lock techniques supported by the Interlocked class on data types that are a fraction of the native processor word size is difficult. The RISC approach to cpu design that was popular 10+ years ago discouraged it strongly. The mismatch between operand size and native memory bus width makes it very hard to implement. One reason that Intel's x86 architecture is still on your lap, surviving 30 years already by not taking the shortcuts. More background info on RISC in this wikipedia article.

Not answering the question, but as a workaround you can just use int instead of bool the way C does.

    int m_IsFirstTime = 1; // 1 means true 0 means false. 

    void SomeMethod()
    {
        if (1 == Interlocked.Exchange(ref m_IsFirstTime , 0))
            // Do something for the first time.

        else
            // Do something for all other times.

    }

P.S. If there is evidence that read is faster than write then Interlocked.CompareExchange might be better for this case (only one first time and I assume a lot of non first).