Depends what sort of juicer you have, mine is an omega vertical slow juicer, which I do always leave out on the worktop. I always fill with warm water and leave it turning, with exit closed, then all I need to do is wipe after emtying. I juice vegetables in mine
Yes there will always be a cloudy appearance and staining from carrots but as long as the tiny holes are clear then really nothing to worry about. A false teeth tablet would probably work, followed by a gentle scour with a dish pad, or try some bar keepers friend and a gentle scour
Other than that, make a cover