Well, I'm not too sure about "complete combustion".

Due to practical matters such as valve overlap and such, combustion is far from complete under *any* engine operating regime. If anything, combustion is probably more complete under wide-open throttle than at any part- or closed-throttle condition. Remember that theoretically, a Carnot-cyle engine maxes out at about 35% efficiency. Empirically, we know from exhaust gas analysis (and state emissions tests) that there are unburnt hydrocarbons in the exhaust stream, which of course we try to minimize with feedback schemes (like the Lambda-sond with oxygen sensors) and catalytic converters.

However - on the practical side: The cat heats up in order to do its job, but it heats up pretty much in proportion to the total inflow of exhaust gases. On a closed throttle and low engine revs, the airflow into the cat is at a minimum, a small fraction of what it is at WOT and high engine revs (and the cat's design of course has to allow for max airflow). So the cat will not heat up as much at idle (given a properly tuned engine) as it will under heavy load conditons. Countering that is that the flow of cooling air over the cat will be minimal, possibly zero, at idle, since the car will either be just creeping or will be parked. Hence the net effect is that with protracted periods of idling, the cat may heat up nearly as hot as it does under full load. Whether this actually reduces the cat's life is a different matter entirely.

I think the best answer to this question would lie in the statistical data regarding the rate of replacement of catalytic converters for fleets with high idle cycles (taxis, police cars) versus fleets with cars which are actually driven most of the time.

The seat of my pants tells me to avoid regular, protracted periods of idling, but I would not obsess over an occasional 10- or 20-minute idle.