1) That quote "Life would continue as before — or even better." is not even the conclusion in the Nature report. It's in the fifth paragraph of the first part out of the three part report. I guess this author just stopped here and failed to read the rest parts of the report for his conclusion?
2) The other two parts of the reports talk about the mosquito biomass and its impact to arctic tundra ecosystem, food chains and even cacao pollination.
3) The original author Janet Fang actually concluded the report by quoting entomologist Joe Conlon "If we eradicated them tomorrow, the ecosystems where they are active will hiccup and then get on with life." And the more important part is the next sentence: "Something better or worse would take over."
The key is that there is a high probability something worse would take over when you tried to mess Nature's arrangement in the past 100 million years abruptly. As noted by other HN user, Chairman Mao also thought getting rid of sparrows was really a good idea.
[1] http://www.nature.com/news/2010/100721/full/466432a.html