I think it's clear from reading his book that Amaral simply didn't have the dynamic mind and mental flexibility to handle an investigation as complex as the one he found himself presented with. Nobody, not even Kate and Gerry, would try to argue that the police shouldn't explore theories. Amaral and his colleagues were right to question the statements made by the McCanns' holiday companions. They were right to scrutinise contradictions and of course, they were right to consider the possibility that the parents or friends were involved in their daughter's disappearance. However, within the first twenty-four hours, certainly within the first forty-eight, they should have eliminated the parents from their inquiries. They failed to do so.
Amaral's problem was that he became fixated, to the detriment of the investigation. He misunderstood the forensic evidence, hardly surprising given that the local officers were trying to gather it without even wearing gloves! More worryingly, he grew increasingly paranoid about the motivations of his superiors and his British counterparts, seeing plots and hidden agendas everywhere. In short, he was not fit to carry out the role entrusted to him by the good people of Portugal.
The above was clear to anyone who had so much as a passing interest in the case. For Kate and Gerry - at the centre of it - it would have been painfully clear that Amaral had all but abandoned any sense of objectivity, and was interested only in his own pet theories. Their decision not to indulge his idiocy any longer was perfectly understandable.
Reconstruction? The only thing that needed reconstructing was the investigative process!