Why was the show so syrupy-sweet and saccharine in the first place?
It was even like that in the first season, which you could argue, was more adult in its humor. Was it an edict sent down by the executive producers, Thomas L. Miller and Robert L. Boyett, since making heavily sentimental yet broad comedies was their specialty, dating back to their days working with Garry Marshall at Paramount?
I don't know how much direct creative control the creator, Jeff Franklin had over the finished product. But according to the Full House Reviewed blog, his brand of humor was more raunchy and subversive as evident in a couple of films that he wrote in the '80s like Summer School and Just One of the Guys. Franklin's original concept was to have three comedians living together. I'm assuming that's why they went after actual stand-ups like Bob Saget and Dave Coulier, whose character is really the only remnant from the original concept.
But it was around the same time that Three Men and a Baby became a smash hit, so the show was more or less, retooled into something similar to that. Plus, sitcoms in the '80s were for the most part, getting decidedly less edgy, hard hitting, and confrontational when compared to the ones from a decade prior.
There's a Reddit post where one of the writers for Full House. And he talked about how everyone basically hated working on it but it was so popular and lucrative they just took the money.