I'd imagine mostly because it's not really relevant, and the media at the time wasn't the tabloid circus that it is today.

Among King's lovers was Georgia Davis Powers, first black senator of Kentucky, who wrote about their affair. According to her for instance she slept with him the night before he was assassinated at the Lorraine Motel. She was climbing into the ambulance to go with him until another individual reminded her of how inappropriate it would be. These are some pretty specific claims coming from a reputable source with 0 motivation to lie, that could be easily falsified.

The letter also mentions another lover by name and implies there was an attached audio recording of King with the classy phrasing, "Lend your sexually psychotic ear to the enclosure..." That audiotape is set to be publicly released in 2027. And then there is the bio of Ralph Abernathy, King's successor at the Southern Christian Leadership Conference and the man King described as "the best friend I have in the world." Within his bio he discussed King's (and his own) regular infidelities.

Because we like to imagine that our heroes are perfect. Martin Luther King, Jr. was an heroic defender of civil rights for blacks; he also cheated on his wife & plagiarised. His misdeeds don't make his deeds any less great, but … we don't like to think about them.