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You might be right that it is not worth adding the ability to handle a variable number of parameters in the new gcd. But this depends on whether you are right that this would add a significant burden to the implementation. I am not sure that it would.
But for pure Python implementations of gcd and gcdm:
def gcd(a, b):
 while b:
 a, b = b, a % b
 return a
def gcdm(a, *r):
 for b in r:
 while b:
 a, b = b, a % b
 return a
using the second of these alone when compared with the first plus reduce on a 10000 length sequence of random numbers in 0 <= r < 10 ** 12 gives speed improvement of over 25%. 
And, since we are looking for speed improvements, a further possible 25% is a worthwhile gain for a common pattern of gcd use. Which is why I believe it is worth asking the question.