Between the two outcomes (ABPs exist but there's no decline, and ABPs are removed but dementia persists), the prevailing interpretation is that ABPs alone do not cause Alzheimer's. They seem to arise along with the cognitive loss, though not cause it.
Tau deposits and associated neurofibrillary tangles have also been implicated in dementia, but also can be absent in those with the disease, so they too are not directly causal.
However, I have not heard of the opposite: people with cognitive decline and amyloid-β pathology but no tau pathology.
Once dementia sets in, there is no turning back, the neuronal network has been damaged enough and you can't replace neurons (not most of them)
Dementia is the main symptom of Alzheimer. And there are other causes of dementia, too.
To continue with your example, if beta-amyloid was a major source of inflammation, and inflammation caused the damage, it'd seem reasonable to expect that removing the plaques would result in slowed cognitive decline.
Strangely, this does not seem to happen in clinical trials.
For example (making this up) I don't think we have disproven that beta amlyoid build-up causes inflammation, which actually causes the brain damage via a process that continues even once the beta amyloid is gone.