Actually, the reason Harry doesn't like to cast fuego without is blasting rod is because Fuego is one of his Rote spells.

From YS257+YS258: Focus items add their bonuses automatically if they are tied in to
the rote, but there’s a caveat: if the wizard does the rote with the focus item, then that item is a requirement for the rote every time he wants to use it. (This is why Harry gets so nervous about entering combat without his staff and blasting rod—he loses the benefits of the rote spell and has to roll each spell as a normal evocation.)