I have three things to add to the existing answer set.
First, 'had inherited' is in the past perfect tense, which indicates that an action is completed, but Harry Potter hasn't yet completely inherited the gold from his father.
There is no mention that he's even received the key that's necessary to access it,
and the only time he accesses it is with adult supervision - let's remember that he's still a minor, even by wizarding standards.
Second, there's no indication at this point of the source of that gold.
Hagrid left it at "It's all yours", so for all we know the gold came from his deceased maternal grandmother, not his father.
Third, it's possible that, since this statement is written from Harry's point of view, it could just be part of Harry's general indifference to money.
Would Harry remember a pile of gold out in Gringotts when he's concerned with a risky venture in Hogwarts? Probably not.