Today is wood working tool analogy day - that's official
The collet of your router is basically no different to a heavy duty nut and bolt and I don't know about you but if I am going to be undoing that nut & bolt a lot then I will certainly keep it well oiled or greased. If you think about the mechanics of the collet, I am not referring to the Xtreme Xtension here, that nut assembly put significant pressure on the thread so lubrication makes sense.
You hit on a good point about no mention of 12,000 mile service on a DeWalt or the equivelent what ever that is for routers, but manufacturers tend to forget these issues.
The Xtreme Xtension works on entirely different principals, it is primarily an extension, dynamically balanced with a quick release mechaism and a light drop of oil will not go amiss.
So go dip your stick and oil your router collet if it is stiff!