In principle, you don't need to wash it.
But what if you want to break off a piece of bread for yourself? Can't butcher a chicken without using your hands? Touching your lips with dirty hands to pull out a fishbone? You will also prick cookies on a fork?
Wouldn't it be easier to wash your hands before eating and for the rest of the meal not to think if you touched food with dirty hands, but to eat quietly.
Washing your hands before eating, after using the toilet is a good habit. As well as observe traffic signals. The meaning of habits is precisely so that you do not need to make a decision on each episode. So that you can distract yourself, think, and still perform an action on the machine that is useful for you in the overwhelming majority of situations.
Well, yes: you can cross the road at a red light, and hands or Do not wash vegetables before eating - most often it does without consequences.
Cutlery is designed to avoid touching food with your hands.
Please note that in Islam, hand washing is very important, therefore in many Muslim countries they still eat with their hands (they went even further and began to use only their right hand for food, and for dirty deeds - left). Europeans, on the other hand, began to wash regularly only recently, so cutlery has long been very important for them, which has become entrenched in culture (without them there would have been more epidemics). For similar reasons, chopsticks are used in Asia.
But washing your hands is also important. After all, some products are still taken by hand, napkins are taken by hand, and much more. In addition, hand washing is not only personal hygiene, but also public. Imagine that someone before you brought your fork to the table with unwashed hands, or cut bread with dirty hands, or someone even washed their hands, but then covered their mouth when they sneezed. Imagine now that this "someone" is you. So respect other people too.
Conclusion: it's better to wash your hands and use cutlery.