Many customers do use TImesheet Approval processes.
I too like the automatic approval process but if you are holding managers (project and or resource) accountable for the time posted you may not want to use automatic approval.
Note: Since timesheets is not an object, you cannot make a process which can be initiated manually. This means if an attribute gets locked through the process and the process gets stuck, you cannot manually unlock the attribue through a second unlock process. You would need to delete the locked attribute. There is a KB on this, but support would need to be engaged for the delete statement.
Also, when using a process you would need to determine if 1 or all approvers need to approve the action item in order for the steps to progress. If you are using Project Manager approvals, and the resource charges to several projects and all project managers need to approve, this could hold up the approval. There are escalation options available, but this could still hold up the approval.
If the timesheets only need resource manager approval, you could give instance or obs rights and not use a process at all.