I have learnt how to compute par yields in class, but I am not certain when knowing this would be of use and by Professor himself said it's a somewhat useless concept. What is the use of computing the par yield? Where does the concept come from and where is it applied?
Quite surprised at your professor's comment, since the par yield curve is one of the most important yield curve representations!
You can of course just plot the yields of coupon bonds against their time to maturity and call it the yield curve, but the curve won't be smooth because of coupon effect (e.g., when the yield curve is upward sloping, high coupon bonds have lower yield) and because of idiosyncratic behaviors of individual bonds. The par yield curve completely removes coupon effect, making different points of the curve more comparable. Further, many par curve models are constructed to reflect fair value of the market, making them immune to local rich/cheap of individual bonds as well.
In practice, traders frequently analyze curve trades (e.g., 5s/10s steepener or flattener) or butterfly trades (e.g., 5s/10s/30s) using par yields. Effective duration is mostly commonly calculated by shocking the par yield curve. The par curve is also used as a reference for pricing new issues.
Academics prefer zero coupon rates because they're simpler. But they're much less tracked by practitioners.