> That's no longer a simple iterator; it's a collection wrapper that represents in-iteration collection.

I am not using a language with iterators in daily work, but that doesn't sound like a real problem to me. The iterator is already provided by the container type and the container already supports removing things:

    iter<T>::drop_current () {
        this->container.remove_at (this->index);
        this->index--;
    }

> Also, how do you solve the problem of mutation done through the collection without involving the iterator

Same like you solve mutation done to the container while the iterator exists, when the iterator doesn't allow mutating. That problem already exists.

I fail to see how mutating a container while iterating is more likely to be a bug, than mutating any other thing.