I don't think it needs any explanation why this trope fell out of popularity. But for a while during the 1970s and early 80s, a TV character couldn't board an airplane and NOT get pressed into service bringing it to landing. It's a trope that cut across almost every genre of TV in that era.

\- Charlie's Angels - "Angel Flight" (s2, ep4) - The Angels go undercover as "stewardesses" (they were still calling them by that title then) and Kelly Garrett has to land the plane after the cockpit crew are all incapacitated.

\- Laverne & Shirley - "Airport '59" (s3, ep1) - In the most contrived use of this trope, the girls take their first flight together. Laverne is afraid of flying and so Shirley tries to calm her nerves by introducing her to the flight "crew." They just blithely stroll into the very roomy cockpit, where the pilot breezily explains that there is no co-pilot because the airline likes to think that "God is the co-pilot" (dunno if that was allowable by FAA regulations in '59, but whatever.) Shirley hands the pilot a cup of coffee during some turbulence, which spills all over him, which causes him to jump out of his seat, which causes him to bump his head, which... (I told you it was contrived.)

\- Happy Days - "Wild Blue Yonder" (s10, ep18) - Not to be outdone by their spinoff show, but the Fonz and Roger (Ted McGinley) take flying lessons from Potsie's uncle. But the uncle bails out via parachute midway through the flight and guess who has to land the plane???

\- Doctot Who - "Castrovalva" (season 19, episode 2) - This trope even worked its way into science fiction! With the new incarnation of the Doctor still delirious following his regeneration, Tegan - who's a flight attendant, mind you - must land the TARDIS! 

[Forgotten trope] Non-pilot characters who have to land an airplane