A tiny object gradually picking up other tiny objects, and the bigger it grows, the more mass it can consume? That's how real planets are formed.
In the first game, all of the stars are 30 meters large at most, while the final level involves making the Moon, which is ten times bigger than that at 300 meters large. This may seem weird, considering how the Moon is thousands of times smaller than even the smallest star in the universe, but it makes sense if you consider that from Earth's perspective, the Moon looks like the largest thing in the sky due to its proximity to our planet.
You roll up balls of objects into stars. Once you get big enough, you start rolling up people. What happens to the people once the Katamari turns into a star?
Katamari Damacy: As pointed out on its own page, everything and everyone who gets rolled up into a star is apparently still alive.
It's heavily implied that they aren't harmed, though, as it has a recurring family that you can roll up in each game, and that even congratulate you when you roll them up into the Moon. How aren't they harmed? Well... it's probably better not to ask. This is further muddled by inconsistencies in what the game will let you do—you can't roll up anything living in the bonfire Katamari, instead setting the hind ends of people and animals ablaze as they run off, but you can roll up living things as the sumo wrestler, which get absorbed, kicking and screaming, into his body. Again, probably best not to dwell on it too hard.
You get to roll up the King in We Love Katamari, and aside from being fresh as a daisy afterward, he straight-up tells you that being rolled up feels good. Of course, he always did have curious tastes.
In Japanese, the word for star ("hoshi") can also mean "planet". Anyone rolled into the Katamari would be living in the now reborn planet.
However, some levels do involve explicitly creating stars, not planets.
Even before you turn the Katamari into a star, the people you roll up go through a lot of pain. Policemen take out their guns and start shooting at your Katamari when they see you, so a stray bullet is likely to hit someone. You can also roll through water, submerging whoever you've got rolled up. Thankfully, game mechanics mean that the guns are harmless and everyone has Super Not-Drowning Skills (including fish that you bring on dry land), but things would get much messier in real life.
Due to the King's backstory being framed as a movie based on his life, it's entirely possible that he and his father actually never reconciled and that he made it to gain some sort of closure on his awful childhood.
.