The issue is historically, we can't take every quote we don't like from Ignatius and say it was forged, because that is the same thing liberals do with the Scripture. Manuscript evidence is admissable and I do agree that we can focus on half the supposed Ignatian Epistles for the reasoning you provided,
But although the shorter form of the Ignatian letters had been generally accepted in preference to the longer, there was still a pretty prevalent opinion among scholars, that even it could not be regarded as absolutely free from interpolations, or as of undoubted authenticity. Thus said Lardner, in his Credibility of the Gospel History (1743): "have carefully compared the two editions, and am very well satisfied, upon that comparison, that the larger are an interpolation of the smaller, and not the smaller an epitome or abridgment of the larger.... But whether the smaller themselves are the genuine writings of Ignatius, Bishop of Antioch, is a question that has been much disputed, and has employed the pens of the ablest critics.
I must disagree with some of this. Though we may prefer some manuscripts over others, we cannot just claim that all of them or fake due to "suspicions." We need better evidence than that or almost the entire historical record is in doubt.
The legitimate epistles contain too many specific details and names, and don't make the outrageous claims typical of the spurious letters. They have common themes about submitting to bishops and what appears to be docetism (which we know to be an early heresy), so it raises an eye brow but it does not prove that they were forged. If Ignatius was wishing to impose, as it appears to be, unbiblical Church government it stands to reason that he would run into opposition.
However, to the best of my knowledge, it does appear that Bishop-led churches with the elders being an inferior branch arose as early as the second century. I have no historical letters that show that elder-led lasted past the first century. In Clement's letter to Corinth, it appeared to be elder led. So, something changed in the 30 years that elapsed between the two letters.
Being that Titus appointed elders, as did Timothy (and Paul), this does not mean that there being an authority above local bodies of elders is entirely unbiblical. However, it appears people started calling these people Bishops and made the church government more centralized.
I am not 100% sold on the elder-led model, as the way it is practiced today would actually contradict how Titus organized the churches in Crete.
P.S. The church I worship in is elder-led reformed baptist.