I was interested in this thread because in Japan, they sell a thick paste (made by Soft 99) called simply "Tire Wax". It is (as best I can tell) the exact same stuff as "Kiwi"- type shoe polish. It looks, feels, smells - and even applies - just like paste shoe polish. It even needs to be brushed or buffed after application to the tire, again just like shoe polish (if you don't buff it, it just sits there, dull and clumpy, like Kiwi would on your shoes without a brushing).
I haven't tried it on trim, but on tires it leaves a very natural matte finish (though a bit "thick", IMHO) that lasts pretty well.
I find the app. process to be a bit of a pain, but for anyone who likes a "natural" look, I would guess that regular shoe polish could be used in the same way, for either tires or (perhaps) even trim.