When is the last time all three had regular-season or playoff games going on at the same time?

This typically happens during the second half of October and early November. MLB playoffs overlapping the middle of the NFL regular season and the start of the NBA regular season.

A regular North American sports equinox, where the four major sports all play on the same day, has happened just 21 previous times. "Thursday is the ultimate nirvana for sports fans as the NFL, NBA, MLB, NHL - plus MLS, tennis and college football - are all in action."This one is a super equinox, with the NFL, NBA, MLB and NHL - plus MLS and college football and that has only happened twice before.

The start of the National Football League season, taken in isolation, is enough to constitute a big day in sports, even if nothing else is going on. A day with a game in a tight, tense NBA playoff series, featuring LeBron James and the Los Angeles Lakers, has the same qualification.

A day with a full slate of Major League Baseball games as the playoffs near, combined with a mouthwatering NHL Western Conference finals matchup, would be a pretty darn good day, too. Well, guess what, they are all taking place on the same day Thursday. Plus, the women's singles semifinals at the U.S. Open tennis championships, a college football game featuring the University of Miami and an appetizing Major League Soccer clash between the Seattle Sounders and the San Jose Earthquakes, and there is simply no reason to move yourself from the couch for anything other than comfort breaks and sustenance.

https://www.foxsports.com/stories/nfl/a-super-sports-equinox-is-approaching

Back on October 28, 2018, all of the major sporting leagues played in the same city on the same day for the first time in US History. Two fans conquered the Sports Equinox in Los Angeles.

https://www.si.com/extra-mustard/2018/10/30/five-leagues-one-day-sports-equinox-los-angeles-dodgers-rams-galaxy-kings-clippers