I've heard that King Toadstool's look was modeled on the King of Grass Land from SMB3, and I guess there is a resemblance. It seems that Grass Land is often regarded as the same as the Mushroom Kingdom, which does make a certain amount of sense. Grass Land isn't exactly a grassland in the traditional sense of the word anyway, since it's full of hills and cliffs.
Even the media that give the Princess father don't give her a mother. For some reason, it seems to be common in fictional royal families for kings to be single parents of eligible young daughters. I think it's common in the Zelda games (as well as the cartoon) for Princess Zelda to have a father, but no known mother. This is also the case for Gwaelin in the first Dragon Quest game, and Marle in Chrono Trigger (although at least her late mother, Queen Aliza, was mentioned at one point). And it's not limited to video games. In a recent post, I talked about Ozma's father Pastoria, who isn't given a consort anywhere in the Famous Forty. And what about Princess Jasmine in Disney's Aladdin? I have to wonder why this situation is so common in fiction.