I've belonged to numerous teams that followed some form of agile, to varying degrees of success (or failure).

The shape of what Agile meant in each of those teams was very different from one another. It would be disingenuous to say "the ones that succeeded were truer to Agile".

If Agile can be summarized as "employ tighter feedback loops", the whole Agile thing was beyond useless. A single sentence, as useful a tenet as it may be, does not a philosophy make. And this idea was not even new by the time the Agile manifesto came out (as explained in the linked blog post).