Protein supplements are just as the name says "supplement".
No, you do not NEED protein powder to reach your daily quota, but the powder provides a convenient source of protein.
Ideally, your diet should have a source of lean protein like the ones you named in every meal. If you're eating enough, it is very easy to reach your daily requirements without the use of any whey protein powder.
Not saying that using the whey is bad or isn't beneficial, it simply is a tool for people who have no time cooking/preparing/buying or simply can't eat enough proteins from their diet to reach their target.
My advice would be to save the money from the protein powder and go buy yourself a carton of eggs and some milk.