Why do people ask for rebalancing instead of doing it themselves? Is it a rule that the swap initiator does a rebalancing when a swap is complete? If so, why is the rule not stated?

The best way to rebalance when a swap is complete is simply to send sats exactly along the newly created route. Only one person has to do this, so it's natural that the swap initiator handles it.
This is not a rule, but seems to be somewhat of a standard that is getting adopted.
Edit: Generally, fees are either set to 0 temporarily for this, or the rebalance initiator is simply reimbursed.

As Fitti answered. It's not a rule on LN+ either.