Amid praise for Stephen Colbert, some ask: What about diversity in late night?

Before the announcement that comedian Stephen Colbert would take over the ‘Late Show’ post, television critics had come up with a number of candidates who are female or black or both.

The choice of comedian Stephen Colbert as the replacement for David Letterman ignited a battle of words online Thursday: While little doubt exists that Mr. Colbert is as funny, clever, charming, and goofy as Mr. Letterman, some media voices loudly complained that the decision by CBS now means that network late-night television will largely remain the domain of white male hosts.

When Letterman announced last week that he will step down from the “Late Show” in 2015, television critics immediately started pooling names of possible replacements: comedians W. Kamau Bell, Ellen DeGeneres, Tina Fey, Chelsea Handler, Tig Notaro, Amy Poehler, Retta, Chris Rock, Amy Schumer, Wanda Sykes, and Aisha Tyler, among others – all of whom are either female or black or both.

“Looking at the hilarious women across the rest of the TV dial – in sitcoms, Comedy Central shows, and Saturday Night Live – the idea that there are no women funny and likable enough to helm a TV show past 11:30 p.m. is increasingly absurd,” Esther Breger wrote in The New Republic before Thursday’s announcement.

But none of the names above won out, causing many to moan that it was just another example of the archaic thinking driving network television, in contrast to cable and online streaming, which supposedly offers a broader range of fare – and faces.

“Clearly, someone out there thinks that it’s just too risky to put a woman behind that desk, that we’re not ready yet,” wrote Ophira Eisenberg Friday in The Guardian. “I'm not sure who that someone is, because I think the audience is there, so it must be someone powerful – an old-school executive, a nervous sponsor, a lazy senior makeup artist. Or maybe that someone just doesn't want to pay to remodel the host’s bathroom.”

Similarly, on Thursday, Don Kaplan of the New York Daily News wrote, “CBS had a chance to make history but chose to play it safe instead.” He said the decision ensures that “late night television will remain an all-white boys club.”

“Sure [Colbert is] one of the smartest, funniest guys on TV and obviously has earned the gig, but these jobs open up so rarely and CBS poobahs moved so swiftly to name a replacement, they missed an even bigger opportunity to change the face of late night television,” Mr. Kaplan wrote.

CBS Entertainment chairman Nina Tassler told Vulture Friday that the network “did talk to everybody – all ethnicities, men and women.” Ms. Tassler suggested Colbert, a seven-time Emmy winner, made the cut because of talent, not his skin color.

“We had a completely diverse group of people being talked about. But you have to make a decision that’s the best choice for the job. And Stephen was just above everyone else,” she said.

Not everyone is mourning. Writing in Slate last week, Amanda Hess said that late-night television talk shows are “stuck in the past” and that hosting jobs are often thankless, one-dimensional roles.

“Late night talk shows are celebrity self-promotion vehicles packaged with broad, sanitized humor that is highly topical but rarely actually relevant. They’re designed to be funny to everyone, and hilarious to no one. Letterman was the notable exception to this rule,” Ms. Hess writes.

As for the Comedy Central slot that Colbert is vacating: Opportunities abound. In the running, reportedly, are Ms. Handler, “Daily Show” correspondents Samantha Bee and Aasif Mandvi, and comedian Aziz Ansari.