Yes, you can wear a supporter all day, but doing so presents as many risks as not wearing one when you're exercising. You wear a supporter to protect your genitals during exercise.
Is it healthy to wear a jockstrap everyday?
Jocks provide support by keeping everything where it should be and preventing injury. Comfortable. You can forget about “adjusting” constantly and trying to defend yourself when people start raising eyebrows. When you wear an everyday jockstrap, sitting, standing, and walking are always comfortable and relaxed.