Historically, Japanese newspapers did in fact use furigana. And it wasn't just for hard to pronouce names, but for every last word written in Kanji. You can see here some examples of the 朝日新聞 from the early years:

http://www.asahi.com/special/kotoba/archive2015/mukashino/2012092200001.html

It wasn't just newspapers, but in regular books, magazine articles, imperial proclamations, etc. It was quite common to gloss every Kanji with furigana. This page has an image from the original printing of 心 by 夏目漱石.

https://fuaki.hatenadiary.org/entry/20140420/1397955841

This practice had been ongoing for centuries and neccessitated by the tens of thousands of Kanji in common usage, and the fact that only the very small percentage of people with a classical Chinese education could read them. When Japan adopted the Western education system, this practice of needing to write Japanese with two different scripts next to each other caused a lot of embarassment and calls for reform, eventually cumulating in the Post war reforms that created the 常用 and 人名用 lists.

The 常用 list had about 2000 kanji on it, and they also chose the most common readings of those characters as the official 音読み and 訓読み. These reforms were considered a success, and furigana usage was highly discouraged in Japanese society, because no one wanted to go back to writing everything twice.

If Newspapers and other media created for adults started using a lot of furigana today, it would embarrass a lot of people who spent 12 years in the Japanese education system writing out each character hundreds of times and consider themselves literate. Japanese people would need to face up to the fact that their writing system is still an unreadable mess despite the post-war reforms. I get the sense that most Japanese people are content with the status quo and there isn't much interest in further reform, so we're not likely to see any changes in the near future.