Moody was the one who gave Harry the idea of him - using the wand and summoning charm for the Firebolt to come right after him.
Then, Hermione and Harry tried practicing the charm as much as possible for Harry to be prepared for the first task, The Hungarian Horntail and the Golden Egg.
There was a part in the book where Harry fell onto some kind of trap, dropping the golden egg, and the marauder's map losing within his reach. Harry, was already having the capable of performing the summoning charm, he could swish his wand and point it right on the parchment and say, 'accio' or 'accio parchment' or 'accio marauder's map'.
With that, Harry could prevent Crouch Jr. (without knowing he was using the potion) from borrowing the map and getting himself into more trouble, especially when Snape and Filch came rushing to the scene.
SameThe same with the goblet (which is charmed to be a portkey). Harry, at the time when he wanted to win the Triwizard Tournament, should have reached the cup before Cedric does. Didn't it ever cross his mind to use the Summoning Charm so that Cedric has no chance of winning at all (removing the knowledge about the portkey)?
In a summarized clarification, the Summoning Charm willwould be a 'overflowing benefit'significant benefit for Harry, if he used it properly and for circumstances like this.
Why didn't Harry use the Summoning Charm for exceptionally significant matters?