The reasons behind the difference in structure are important.
While they won't easily admit this, it has only been since and as a result of the social egalitarian movement (Civil Rights and nondiscrimination in general) that the fundamentalist, charismatic, and pentecostal churches have somewhat shed their image as a reservation for poor and uneducated people. The megachurches were born.
While some folks built megachurches, others looked around and saw paid for Episcopal churches on prime, often historic, and socially advantageous real estate with dwindling membership. Having been in the catbird seat for so long, many of these churches were physical centerpieces of towns and also had considerable bank accounts. They became targets for takeover.
Truro Church in Fairfax and another old church in Pittsburgh were perhaps the best known churches to be stolen by people who deliberately joined the church, brought others with them, and then took it over. For this reason the Episcopal Church went to court to establish its ownership of all church property.
If Muslims were pretending to be Baptists to steal churches, Americans world not approve. Converts stealing Episcopal churches is no different.
Another phenomenon out there is Catholics who want out from under some rules going to Episcopal churches and then trying to make them more conservative. Kind of a "ok I can be a priest and get married, but you still can't be gay."