In the first Dune book, we see House Atreides pack up and move permanently to Arrakis, even though they clearly have deep ties to Caladan. We also learn that the Harkonnens were allowed to maintain Geidi Prime as their homeworld, even as they had full control of Arrakis. Why couldn't Leto stay on Caladan with Jessica and Paul, and send Duncan or Gurney to govern Arrakis, the way Raban was doing so on behalf of the Baron?
The Harkonnen were simply under contract to supervise the mining of the spice on Arrakis whereas the Atreides family were given the planet entire, including the responsibility for mining the spice.
Since the rules seem to be that you can only have one planet as your fiefdom, this meant that they had to give up Caladan.
Thufir Hawat, his father’s Master of Assassins, had explained it: their mortal enemies, the Harkonnens, had been on Arrakis eighty years, holding the planet in quasi-fief under a CHOAM Company contract to mine the geriatric spice, melange. Now the Harkonnens were leaving to be replaced by the House of Atreides in fief-complete — an apparent victory for the Duke Leto. Yet, Hawat had said, this appearance contained the deadliest peril, for the Duke Leto was popular among the Great Houses of the Landsraad.
Note that the Baron's plan was not to gain the fiefdom of the planet (since no House Major can have more than one planet) but to gain a sub-fiefdom, independent control in all but name.
Piter shrugged. “If matters go as planned,” he said, “House Harkonnen will have a subfief on Arrakis within a Standard year. Your uncle will have dispensation of that fief. His own personal agent will rule on Arrakis.”