I've heard the same, but it really feels like a naïve take. We can't know for sure that they have no positive purpose in their ecosystems, and eradicating them is a one way street.
No idea where the belief came from, but it's a bit concerning how widely held it is.
With Dengue, if the body is exposed to multiple strains within a short time period, there's no severe reaction.
However, if there's a delay, and the body gets to prepare, and then sees a slightly different Dengue virus, the shit hits the fan.
So the decreased number of mosquitos left a greater mean time between cross-strain exposure, which in turn increased the number of severe reactions.
If so.... the resurgence in populations is what caused the increase.
This article (The Autoimmune Mechanism in Dengue Hemorrhagic Fever) https://pubmed.ncbi.nlm.nih.gov/29686179/ is probably more relevant.
Why cross-strain exposure would prevent that auto-immune reaction, I have no idea - probably something to do with tiny little puzzle pieces that almost fit.
(And no real need for the condescension.)