I know that Catholic and Episcopalian scholars don't believe that - in fact, anyone who has a cursory knowledge of the early church and the church fathers can trace significant developments in church organization and theology.
The theologies of the Church have changed significantly over the years, typically about 20 years [and sometimes a lot longer] behind popular philosophy.
The early church is not something to try and immulate.
certainly , while the Anglicans would claim links to the early church through both the Celtic and Catholic churches, and there is significant evidence of even earlier links to the Coptic monastic tradition dating from the 200's AD we know we are not following some fossilised religion, but are part of a living one that makes itself relevant to each new generation.
We still learn much from Jesus teachings, and they can easily be show to have relevance to modern living, but perhaps in ways that would surprise an early church father.
It is true that Heretic members, like myself, who have moved perhaps faster than most from the traditional ( 18th century ) CofE, do not represent much in the way of a proportion of the church today. However we do perhaps lay on a trend line in the direction it is going.
Is this good or Bad ? who knows... it may be a false trail.... but it is a live one.