Tights are worn in ballet because they are functional.

Ballet requires movement of the entire body, and tights and leotards (or unitards, etc.) allow free, usually unhindered movement.

In addition, tights et. al. allow the teacher, observer, etc. to see the muscles of the body in full action.

Nowadays tights et. al. are made from materials that are very flexible and which adhere closely to the body.  In older days, before nylon and other fabrics that allowed full "stretch," dancers wore fabrics like the cotton-based moleskin, which allowed for some stretch, but could be confining.

Earlier than that, tights and "bodywear" had to be "seamed" in the joint lines to allow for movement, but this still did not allow for unhindered movement at all times.

Once again, the major reason for tights and bodywear is to allow full functional movement and allow presentation of the muscles, joints, etc. so that the teacher and observer can appreciate the full function of the body in dance.

Don't ask why people don't dance nude!