While removing and cleaning the filter material may help lower the nitrate, what you are essentially doing is only exporting the nitrates just like a water change or pruning macro-algae in a refugium. In my opinion, keeping live rock rubble in a filter will end up causing the same issues as having filter material unless you clean the rubble just like the filter material. Live rock rubble will trap the detritus just the same as filter material but it lacks the ability that bigger pieces of live rock has to convert nitrate to nitrogen gas. You will still have to clean and blow out the live rock rubble in the end.
As sporto0 mentioned, live rock that is not rubble will convert some nitrate into nitrogen, but not all of it especially in a fully stocked tank. If you want undetectable nitrates, a combination of methods should be used to keep nitrates down. These can include using porous live rock, heavy skimming, a deep sand bed (remote or in tank), denitrifying filter media, a refugium with macro-algae, and an algae turf scrubber. That and of course water changes.
But I don't see what is the harm in keeping nitrates low even if in a fish only tank. It may not harm the fish unless concentrated at super high levels, but it will make it easier to transition to a reef tank if and when the person wants to go to the dark side :smokin:
edit: There was an article that I saw not too long ago that examined live rock's ability to convert nitrates into nitrogen gas, as well as the ability or rather inability of live rock rubble to do the same. If I can find it, I will post a link to it here.