Admitting 1 as a prime number messes up all these theorems, which otherwise have simple statements.  If the messing up accomplished something of real value,  it would be all right.  By this, I mean that if the explanations had to be complicated in order to help people understand some subtle point that was of real interest, that would be all right.  But in these examples and many others, the additional complication introduced by admitting 1 as a prime number does not lead anyone to any better understanding of what is going on.