Disney helped with that trend. Not just SNL members, but comics in general. After their stand up careers ended, Disney put a number of them to work.
Cheech and Chong (separately, not together), and Denis Leary come to mind.
Robin Williams' stand up days were long behind him by the time Aladdin came along, but helped keep him in the limelight.
Gilbert Gottfried's stand up career never took off, and he was voted the worst SNL member ever. Way to go. Your crusty voice and lack of talent paid off in spades.
Tim Allen's success as Buzz Lightyear (and Santa) killed off his stand up career. I saw him back in 1990, before "Home Improvement", before hitting the big time. His star was rising fast. He was hysterically funny, but incredibly raunchy, un-PC, and maybe even a little drunk. (Still had me in stitches, laughing so hard my jaw hurt).
After the Toy Story movies, he tried his hand at stand-up again. There was a new generation of fans who brought their kids to his shows, but he had to sanitize his act so much, he gave it up after a while. Imagine the shock of the voice of Buzz Lightyear talking about women's parts. GASP!
George Carlin didn't have to worry. His voicing Fillmore in "Cars" was a side trip, then he went right back to telling people to go "F" themselves. Good ol' Georgie.