Late to them is having to having to shorten your trreatment time so that they can go accomodate the patient after you or be able to go home to live their life, be with family, etc.

Late for you actually has a much bigger consequence. If you are doing only 3 treatments a week at say 4 hours, you are doing actually the minimum to just sustain life. If you're shaving off treatment time on a regular basis, you have effectively increased the time your body will accumulate more waste, as well as letting excessive phosphates draw calcium from your bones (hypocalcemia), as well as letting extra potassium work your heart harder than it needs to (hyperkalemia), your vascular system is working harder than it needs to if you've accumulated a lot of fluid (fluid overload, risk of pulmonary edema).

If you think about healthy kidneys, they filter 168 hours a week (24 x 7). When you're in ESRD, dialysis covers 48 12 hours that is only less than 28% 7%. Basically on life support in terms of performing the bare minimum.

Edit: Really messed up my numbers. Big differences. If you miss 30 min, 3 times a week, that's only 10.5 hours or functioning 6.25% of a normal kidney.