> We are told that each king's pyramid and its
> temples, etc., were built and maintained
> completely independent of his predecessors'
> efforts.
> We are also told that some king's were quite happy
> to spend time and effort (even if it only was for
> 70 days) tidying-up there predecessor's complex.
> I find this somehow contradictory, but cannot
> explain why.
>
Continuity.

The AE were desperate to have order & continuity in their lives. Finishing the late king's tomb was an act of continuity & solidarity. You're showing that you respect & honor your predessors. There may also have been rituals associated with doing so which were required before the new king could ascend the throne. Also the 70 days is not set in stone; there were longer periods of time between the death & the funeral. Some of these may have been tied to a murky succession.