This method is known as a “vote count” method of meta-analysis. Thinking about reports in this way is in contradiction to the idea that meta-analysis can maximize power and detect an aggregate effect when individual studies do not (as noted in your second point).
It was mathematically proven to be biased against finding true effects by Hedges and Olkin in their classic Statistical Methods for Meta-Analysis
A better method is p-value combination, as I’ve mentioned in other threads. These generalize to modern “fusion learning” and “confidence distribution” methods.