I do not think you need to stick to a strict schedule, but it may help if you tend to be as disorganized as I am. My schedule varies wildly from day to day, so having a stricter schedule for my pets helps keep them healthy.
I organize the fish food and feed it in rotation so they get higher vs lower protein, algae based vs animal based foods and higher in the tank vs sinking foods in a rotation. That way if some fish do not like the food that day, they will probably eat the next day. Same idea with water changes. When I was following a schedule of large, frequent water changes I stuck to a schedule that rotated through all the tanks.