nitrates are not the only things that get in the tank that should be removed.
Firstly, your water's buffering capacity needs to be refreshed. The end products of the cycle are acidic, and given enough time without refreshing the buffers, your tank will drop in pH, sometimes very quickly. Given the other benefits of a water change, I feel the best buffer refresher is new water, instead of chemicals.
Secondly, there are tiny concentrations of all sort of other things in the tank that cannot be healthy for your fish. These chemicals are in the air and some of them do eventually make their way into your tank. I am talking about things like cooking oil, cigarette or candle smoke, carpet fumes, fumes from cleaning products, and many more. For people, all we have to do is open a window and clear the air. But, small concentrations of these get in the tank, part per million, parts per billion, maybe less, and for short times they probably have a negligible effect. But, if you don't change some water out, they sit in there, and build up, and I cannot imagine that they are good for the fish's long-term health.
Finally, for the sake of the fish, don't they always seem more perky and vibrant after a water change? During certain times of the year, every time I do a water change my corys respond with a spawning event. All the evidence I have ever seen shows that more water changes, the fish will respond will greater health and vitality. I keep fish to try to keep a little slice of nature in my home, and while it is impractical for most of us to do continuous water changes like nature provides, that water change is trying to approximate nature.