First, I don't think the Protestant rejection comes from our desire for no intermediaries in our relationship with God. You are right to point out that we do believe this. However, I think our rejection of the doctrine of Transubstantiation is that it is culturally bound to a time and a way of thought with which we are not familiar. It is tied implicitly to Aristotelian thought. And as our theologically distinct movement began somewhat later and in a different culture, it makes no sense to us.
Of course, that means we make our own mistakes with respect to our culture and our time, but that is the ever-present peril of translating the sacred and transcendental into human vocabulary.
Secondly, if Ignatius was addressing that to those who did not want the authority of the bishop (a point he makes repeatedly and could have just as easily inserted there, too), I believe it would have much more strength. Indeed, it would be irrefutable (except to point out that it's not in every version of the letter).