It has nothing to do with your water quality. Most medications start to break down and react with stuff pretty quickly, and produce byproducts. For example, if you were using a formalin based medication, you'd get formic acid and methanol, as well as high CO or CO2 levels (though that could be driven off with an airstone). Malachite green breaks down rapidly in water (with light) to form leucomalachite green and oxalic acid. Leucomalachite green is incredibly lipophilic -- meaning it is absorbed by the fatty tissues of fish at a much higher rate than regular malachite green, and bioaccumulates. Oxalic acid binds with calcium in the body, interfering with fish's ability to build bones (you can screw up your own calcium levels by eating foods high in it, such as spinach and beets, though it takes A LOT...). Some antibiotics and other medications also produce other acids, which can crash your pH if you let them accumulate.
On the other hand, some medications, like erythromycin, tend to stick around in the aquarium. Without water changes, you're simply drastically increasing the levels of them -- which means you can suddenly crash your biofilter, as well as leaving constant trace amounts that contribute to antibiotic resistance.
You really want to do large, regular water changes when using medication to remove byproducts and residuals -- personally, I don't think 25% daily is adequate. (And, in many cases, large water changes have an /incredible/ beneficial effect on pathogens -- you can actually wipe out ich with water changes).