Of all the formats native to television, the late-night talk show may be the one most bound to the structure and conventions of old-fashioned TV. You switch on a specific channel at a specific time; you have a standing date to watch a host talk to interesting stars (or make boring stars interesting); you go to bed.

So the genre has had an especially tough time adjusting to an era where the TV channel is just one media pathway among many. Who needs a late-night chat with the stars when stars are available on Instagram and Twitter, 24/7 and without intermediation? What is “late-night” talk on a streaming platform, where, as on a casino floor, neither day nor night exist?

I’m not sure anyone really knows the answer, which is why, even as talk shows have multiplied in recent years, many have struggled.

But the attempt to figure it out is the most interesting thing about “Busy Tonight,” Sundays through Wednesdays on E!, and “Patriot Act with Hasan Minhaj,” Sundays on Netflix. Each is adapting an appointment-TV staple to a phone-scrolling, binge-watching era in a different way.