Mold will grow on damp cotton clothes -- not enough to see with the naked eye, but some people are more sensitive.

Also important: some people live in areas with higher ambient humidity than other areas. If you live in an area where swamp coolers are a viable option in the summer, then of course you'll have trouble understanding why some people don't see hanging up damp clothes to be a reasonable option.

When you put these in a drawer, they don't dry. They get moldy.

Right, so you hang them, briefly, until they do dry. Then you put them away as normal.

With the premium that house space demand, a cloth track, even a foldable one, can ruin your living space for hours a week. And since there's a strong correlation by laundry and weekends, you'd get your living space stalled the days you need it the most.

Or, do the simpler thing and make sure they come out dry from the dryer.