I personally disagree that water changes are the only way, and I also disagree that nitrates over 100 will cause fish to get sick. It is not good, but it will not cause immediate harm (this is from personal experience). Corals are another issue. Regardless, you should be aware long before nitrate levels ever approach this point and so can readily and reasonably address it. One of the worst approaches to high nitrates (above 100) is rapid large frequent panic water changes, which can cause far more harm than the nitrates.
There are several ways to address nitrates, first and foremost is being accountable, as a hobbyist, for your stocking rate and feeding. Many new tanks, especially, are overstocked and overfed. These are the primary reasons for nitrate issues.
Another reason is lack of appropriate tank maintenance. Not enough water changes, allowing gunk to accumulate in sponges, bioballs, etc.
Lack of a protein skimmer can contribute to nitrate issues as a skimmer helps remove stuff that will break down in the tank.
A refugium with macro algae growth is another export mechanism to help with nitrates. A deep sand bed, and significant amount of "larger" pieces of LR will aslo help address nitrate levels.
Water changes, without a doubt, are important...but there are ways to address nitrates before you even get them.