Because it is stated in one of the rules that a god of death or shinigami cannot go to the Human World without any clear or significant reason. As stated here,
The god of death must not stay in the human world without a particular reason. Conditions to stay in the human world are as follows: (Death Note - How to Use It: XXIV)
- When the god of death's Death Note is handed to a human.
- Essentially, finding a human to pass on the Death Note should be
done from the world of the gods of death, but if it is within 82 hours this may also be done in the human world.
- When a god of death stalks an individual with an intention to kill
them, as long as it is within 82 hours of haunting them, the god of
death may stay in the human world.
If these rules or the rest of the other rules not mentioned are violated, then they will be severely punished. That's why Ryuk was hesitant at first when writing the fake rules Light asked him to since he thought it might anger the Shinigami King.
There are laws in the world of gods of death. If a god of death should break the law, there are 9 levels of severity starting at Level 8 and going up to Level 1 plus the Extreme Level. For severity levels above 3 the god of death will be killed after being punished. For example, killing a human without using the Death Note is considered as the Extreme Level. (Death Note - How to Use It: XLVI)
In case you're wondering where these rules are since these might not be in scanlations or unofficial translations, the official English VIZ volumes that I read have them in-between each two chapters.