I went to school at a relatively late age and started in community college. The school/state had a policy where any independent income earners making less than 35,000/year would not pay tuition. A single dollar over that would require paying full tuition of ~$60/unit or about $750 a semester. One year I worked a little more overtime during the holidays than usual and realized with a week to go in the year that I'd go…
They often do use sliding scales, but that’s more complex (and expensive) to administer, and (because of multiple interacting programs) ends up not actually solving much of anything. Also, because of the way things (including available funds) work, but even ignoring budgeting for the increased admin cost, a sliding scale probably would start stepping down from full benefit where a sharp cutoff is, that would probably be more like the middle of the sliding scale, so if you “barely squeaked in under the limit” on the sharp cutoff version, you’d probably get far less benefit under a sliding scale system.