The Washington Times has always been part of the conservative vanguard against communist media bias. (Though I personally think it's become increasingly worse over the end of Bush years into the Obama years, it used to be a bit more of just a conservative spin on things with conservative columnists, much like Fox was. Though like Fox, the occasional white supremacist or something would sneak in, I don't feel like the Times would have been publishing regular stories about stuff like Seth Rich or a lot of its inflammatory-focused immigration restrictionist content 15+ years ago. It wasn't favorable to Pat Buchanan for example.)
I imagine a large part of the The Daily Caller's increased prominence on Fox comes from the fact that Tucker owns it. (Or did?) Plus it seems to be a key site for the "scoops" of the conservative press these days. Like it was the first site to dig out that Bill Kristol had finally decided to grab the Infinity Stones himself, and he actually replied back to it, even Democratic or progressive organizations will respond to its inquiries. Some of it isn't entirely terrible, like how BuzzFeed would always have those one or two semi-legitimate reporters, TDC has a few of those. It also has benefited from Hot Air's more prominent editorial voices regularly bashing Trump and running anti-Trump stories.
I think there's tensions within Fox because its original main sources for conservative voices like the Wall Street Journal are at best Trump-neutral on key issues, so are lots of the think tanks it used to mine, while the audience wants lots of Pro-Trump coverage. So they're having to turn to a lower tier of guest and source. Along with social media superstars like Diamond and Silk.