This claim does not appear to be grounded in any factual basis: A double-blind randomized trial for an mRNA vaccine with 44k participants showed nearly identical all-cause mortality in vaccinated vs. placebo groups after six months [1]. The delta wave will almost certainly be less fatal, but there is no evidence to indicate that widespread vaccination is the primary causal factor, or even a contributing factor, for the reduced mortality.
[1] https://www.medrxiv.org/content/10.1101/2021.07.28.21261159v...