Although electric towel radiators can be left on continuously, which is not recommended in the case of single-heat elements, it's not always necessary and may not be the most efficient use of energy.
Obviously, being continually on means continuous energy consumption and higher energy bills. You can help navigate this by utilising the timers and programmes that most elements have built in. Turning the radiator on a short time before you need it can be an effective way to use energy more efficiently. Or have it run for 2 hours over night when electricity is cheap to dry your towels.