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I wanted to chime in on the why of the matter as well, so there's no guesswork involved in using filter setups either for marine or freshwater tanks and picos/nanos.
In some filter additions and styles such as canister filters you have mechanical benefits such as particulate removal that have nothing to do with nitrate production when this benefit (clearer water or additional movement) is combined with the cleaning schedules that prevent detritus/nitrate buildup (nitrate factory). Guys like ninja needed this type of filter as a refugium and both as a water pump in his cube, there's one setup where a canister filter was critical. Many systems are designed where the rock is sufficient enough and extra surface area is not required, per your ammonia test outcomes.
In your case a wheel only offers one type of filtration for the most part, surface area boosting, which is strictly needed if bioloading outpaces tank surface area and ammonia production is the problem. If you have ammonia still in your cycled tank, then you'd need it because you aren't oxidizing primary wastes quick enough, without ammonia (including both fresh and marine systems) you do not need it. If you are testing and getting no ammonia or nitrite but are getting nitrate, your surface area is sufficient per that loading and you can now move to water changes, refugia or more complicated anaerobic bacterial systems to remove the nitrate. These are not practical in our world of nanos where a water change is far simpler, but I have seen them used before.
The live rock in your system is no different than your sponge filter or wheel sponge, it's just a little easier to blow clean regularly. If it is not cleaned of detritus regularly, it becomes a nitrate factory too, just like filters, because once again you have massive surface area accumulating detritus in the cracks and pores and as that detritus degrades further, the protein aspects of it once again are broken down into ammonia and other wastes which are put back into the system. There may be some anaerobic NO3 degredation going on just inside the rock's surface which you don't get in a biowheel or a canister, but the rate at which you blanket it with waste (in a nano) far outpaces that natural nitrate removal. Nothing is a nitrate factory if you scrub it clean at each change with saltwater, only detritus and protein degredation causes nitrate factories, that needs to be understood by the masses.
You can have an aqauarium with ten biowheels on it, as long as you keep them clean of mulm and follow strict servicing guidelines your tank will register nitrate the same as if you had no biowheels as long as the bioload is reasonable per water volume. It all depends on cleaning hassles, most people don't clean them as they should so in time as the wheel becomes brown with mud, you can literally see the little aggregations of bacteria and nutrient that will in turn leak as nitrate.
On that mark, leave off the biowheel
B
