Why do microwaves run 3 extra seconds after timer ends?
I had a microwave oven that would keep the fan, light, and turntable going until the food was rotated to its original orientation.  That way it was easy to grab the handle of your tea cup :)

I've repaired microwave ovens in the past, and I don't think that a few extra seconds of airflow (after the cooking is completed) would help the longevity.  They are designed so that nothing gets hot except for the food.

Unless, of course, it is a dual microwave/convection model.  Then a cooling cycle would keep the hot elements from over-heating the convection pathways.



Update:

I've been doing some research and have found additional information.  The microwave ovens are not actually all that efficient from an electrical power standpoint.  For example, a representative oven I found online cooks at 900W but requires 1350W from the wall outlet.

This relates to your question because all that extra power is dissipated in the oven as non-functional (not-for-cooking) heat, and is removed with fans.  Most of the excess heat is generated in the magnetron, and a little is used for the controller, user interface, etc.

Removing some of this waste heat from the magnetron may very well improve the longevity of the oven.  The design engineers may have reduced the oven's passive venting by including extra active fan-based cooling.