Has variety sketch peaked? This year’s Emmy category got caught in the rule change that limited the number of nominations in proportion to the number of contenders submitted — and with just 14 entries, that meant only three ballot slots. Several of last year’s nominees (“Documentary Now,” “I Love You, America With Sarah Silverman” and “Who Is America?”) weren’t eligible in 2020, while “At Home With Amy Sedaris” didn’t make the cut, leaving room for returnees “Saturday Night Live” and “Drunk History,” and newcomer “A Black Lady Sketch Show.” With previous nominees such as “Portlandia,” and winners “Key & Peele” and “Inside Amy Schumer” also long gone, variety sketch could be at a crossroads. NBC’s “Saturday Night Live” is looking for a fourth consecutive win, but keep an eye on upstart “A Black Lady Sketch Show,” from HBO.