Of the shows you cite, Haganai was animated in 2011; Black Rock Shooter was animated in 2012; and Oregairu was animated in 2013. The source material for each is even older (albeit kind of irrelevant for Black Rock Shooter). I omit Gintama because it's long-running and I don't know when your screencap is from.
Smartphone adoption in Japan is hugely up between 2013 and now, and even more so between 2011 and now. According to the CIAJ (as cited in a whitepaper titled "Japan’s Smartphone Surge and Its Impact on the Mobile Marketplace"), smartphone penetration in the Japanese market was a mere 9% in 2011, rising to 39% in 2013, and skyrocketing to 84% in 2016.
Is it any wonder, then, that anime set in "the present" that aren't from the past year or two would tend to have more non-smartphones ("feature phones", as they're called) than smartphones?
(I specify "the present" because we should exclude from discussion any shows set in the future. They tend to have fanciful notions of how telecommunications would work that don't tend to involve feature phones or what we would consider "smartphones".)
Is it because the authors are just from an older generation than the fanbase? No way, right? They have to have smartphones.
This effect may exist - according to the Pew report "Smartphone Ownership and Internet Usage Continues to Climb in Emerging Economies", in 2015, Japanese people age 18-34 were about 2.5 times as likely to own a smartphone as Japanese people age 35+.
I doubt it is a substantial effect, though. Any animated production involves multiple people with creative input (not just the author of the source material), and I would imagine that at least some of them would know what kind of technology youngsters use.
I don't think that's true (bad evidence alert).
Best Korea is proud of the way you confirm your priors.
Why are flip phones still so popular, (if you can endeavor to answer) in both society and anime/manga?
The article @Maroon linked in the comments is a good overview of why smartphones were not common in Japan (prior to 2014 or so).
And why were smartphones not common in anime/manga? Because smartphones were not common in Japan. Simple as that.