What is kernel_task reading and writing?
As the name suggests, kernel_task is like a task master and does a lot of system tasks for the macOS kernel. 

Reading and writing to disks is one of the tasks it performs, so a lot of system data or app data may be read and written through kernel_task. So obviously it will show a high count. One thing to particular check is RAM usage - if you don't have enough RAM for some task, macOS will create swap memory on your disks and that also will count towards the high read and write in disk activity for kernel_tasks. This can explain what you are experiencing - swap memory read / write are temporary writes and so don't show up as using your disk space.

Chrome is known to be both a CPU and memory hog. Dump it and switch to Safari or Firefox which use less resource.

Note that kernel_task also plays a role in managing the CPU temperature, which may show it as using high CPU in Activity Manager. So if it is showing as using a high percentage of CPU, you can temporarily kill other apps or processes using most of the CPU as they are the cause why kernel_task kicks in (higher CPU usage = higher CPU temperature).