Why do we need a swapper task in linux?
Solution 1:
The reason is historical and programatic. The idle task is the task running, if no other task is runnable, like you said it. It has the lowest possible priority, so that's why it's running of no other task is runnable.
Programatic reason: This simplifies process scheduling a lot, because you don't have to care about the special case: "What happens if no task is runnable?", because there always is at least one task runnable, the idle task. Also you can count the amount of cpu time used per task. Without the idle task, which task gets the cpu-time accounted no one needs?
Historical reason: Before we had cpus which are able to step-down or go into power saving modes, it HAD to run on full speed at any time. It ran a series of NOP-instructions, if no tasks were runnable. Today the scheduling of the idle task usually steps down the cpu by using HLT-instructions (halt), so power is saved. So there is a functionality somehow in the idle task in our days.
In Windows you can see the idle task in the process list, it's the idle process.
Solution 2:
The linux kernel maintains a waitlist of processes which are "blocked" on IO/mutexes etc. If there is no runnable process, the idle process is placed onto the run queue until it is preempted by a task coming out of the wait queue.
The reason it has a task is so that you can measure (approximately) how much time the kernel is wasting due to blocks on IO / locks etc. Additionally it makes the code that much easier for the kernel as the idle task is the same as every task it needs to context switch, instead of a "special case" idle task which could make changing kernel behaviour more difficult.