I don't know what happened to Madeleine McCann. But unlike you and others, I don't see that as carte blanche for mouthing off "my doubts" for over fourteen years.
Something other than "doubts" must drive that and I am interested in what that may be ~ but I sure don't expect any enlightenment to that.
... and as far as the botched first investigation goes ~ I think you have hammered home the nail in that I certainly don't know much about what actually went on.
I think it is an absolute sure certainty that I would be even more appalled by the conduct of affairs did I know even one iota of what went on in the underbelly of the PJ populated by the leaders of the investigation some of whom ended their PJ careers as convicted criminals themselves.
It may have escaped your notice, but there has been a concerted effort to prevent any discussion of the McCann case which didn't uphold the story they told. A wide range of people were threatened in various ways in an attempt to prevent certain facts and opinions being expressed. No stone was left unturned; from dossiers gathered about ordinary people to high profile libel actions against media outlets.
In my opinion those efforts ensured that people found ways of expressing their opinions nevertheless. Why? Perhaps because people suspected that the adage 'no smoke without fire' had some truth in it. The unremitting determination to silence questioners simply reinforced their conviction that speaking out was necessary imo.
The PJ may have made mistakes, and their efforts may have been hampered, but they still trod their own path. Imo attempts were made to persuade them, like Operation Grange, to investigate only abduction by a stranger, but they didn't comply.