The Stanford Encyclopedia of Philosophy's article on Everett gives a much better description than Wikipedia. "Everett's solution to the [measurement] problem was to drop the collapse postulate from the standard formulation of quantum mechanics then deduce the empirical predictions of the standard collapse theory as the subjective experiences of observers who were themselves modeled as physical systems in the theory." Everett's formulation does not have to be viewed in terms of the pop-sci conception of many worlds. The article describes it as a no-collapse formulation.
At the end of Everett's thesis he writes "It remains a matter of intellectual interest that the statistical assertions of the usual interpretation [of QM] do not have the status of independent hypotheses, but are deducible (in the present sense) from pure wave mechanics, which results from their omission." His formulation takes more computational work to produce probability predictions since they are derived and not inherent in the theory. The point is its conceptual elegance doing away with wave collapse.
A real argument for Everett's interpretation would be a testable prediction. The encyclopedia of philosophy article claims that "Everett held that it was always in principle possible to measure an observable that would detect an alternative post-measurement branch." I have no idea if anyone has ever tried to make a concrete prediction from this formulation.