The FPOBA aired at 8 pm on Monday nights and owned that slot. For damn near it's entire run America ran like clockwork on Monday night:
8pm: FPOBA
8:30 pm: Blossom (not as unanimous as Fresh Prince but still owned that slot)
9pm: Monday Night Football (Al, Frank, and Dan Edition)
Will had crossover appeal unlike any rapper did to that point, and was the first to engulf the nation with both his acting and music since The Rat Pack of Sinatra, Martin, etc of the 1950s.
Therefore he didn't need to wild out with curses or violence in his music because he didn't need to market himself to the "rough urban" niche, and he would have been a fool if he chose to do so. Suburban housewives who watched FPOBA buy music too (to paraphrase Michael Jordan) so why not put music out there for them to purchase comfortably and also for those white folk who may have had a curiosity into hip hop but felt uneased by the gratuitous use of the n word. Will Smith's music would have been a perfect transitionary point for both groups.
Not to mention Will the character became such an ubiquitous entity for Will Smith the human that he couldn't go from "All American good kid with a million dollar smile who's living right" from the TV show to "Violent, gun-toting misogynist who don't give a fukk." in the studio. The stark contrast would not have sat well with his consumer base. I was a teen in 90s NYC and can tell you no one was bumping Will Smith at a time qhen Biggie, Pac, and the Wu reigned supreme. Will was doing numbers, so you know it was other demographics grabbing his music at a rapid pace off the record store shelves. We had no problem at laughing at the antics of goofy Will on a Monday night, but would have gave thugged out Will no burn whatsoever on a Friday evening. What started as a character portrayed by Smith eventually became the overarching definition of Will Smith the man just a few seasons in. He WAS The Fresh Prince of Bel Air, no matter how creatively trapped he may or may not have felt.
And in many ways he still is The Fresh Prince of Bel Air, and it's that's identification of him that catapulted him to stratospheres of stardom rarely touched. It's why "The Slap" became a world-stopping moment for damn near a month. The where and what of it obviously contributed, but that it involved America's Fresh Prince as the aggressor (and not, say a Shia Lebouf or Sean Penn, two guys known for hot tempers) was one of those "peel back the curtain" moments of uncomfortable truths that leave onlookers speechless, like the school valedictorian beating someone to a pulp instead of the bully. Up until the Oscars moment America still saw the "Will Smith" who would threaten to smack Carlton jokingly, flash his amazing smile 10 minutes later, and who always came out the good-guy winner at the end of a 30 minute farce. That night they saw the death of that character and it was jarring for many to witness, especially live.
Aggression was never going to be his calling card. Contemporary society has changed for the bleeker and with cynicism ratcheted up we will probably never see a "clean" rapper put up "Will Smith numbers" ever again.