A line cook can't stop what they are doing for even 5 minutes during a 4 hour period of time. There might be a lull for 15 minutes between seatings to run to the bathroom, but sometimes not. It is brutal work. Because of the thin margins in restaurants, they tend to be under staffed. When something needs to be fixed during service, maybe a plumbing problem, the ice machine broke, or a purveyor didn't deliver the correct items so someone needs to run to the supermarket, it is usually the dishwasher who fixes the problem. The pay is awful for a dishwasher. Likely, especially in California, the dishwasher in the restaurant you are eating at isn't legally allowed to be in the United States. Other times, the dishwasher will have a criminal record and can't find other work. Another dishwasher in Portland had his entire face tattooed with body modifications. They are in that position for a reason. The point is paying the dishwasher in respect if not higher wages is important to the survival of a restaurant. A chef depends on this person who is in the lowest social position to have his or her back.
If it's anything like the small, dinky restaurant i washed plates for, the reality is that the restaurant doesn't have enough plates and pans to satisfy every order on a busy night without washing something. Pans in particular are reused multiple times during a shift, and they better be well-scrubbed, because you don't want your fancy ingredients tasting of something else.