In my opinion, the author brings Gatsby's father into the novel so as to give us more of an insight into Gatsby's past and his motivations.
I think Gatz does a couple of things that help us understand Gatsby. First of all, he is very happy about how rich his son has gotten. This sort of helps us understand why Gatsby was so ambitious -- it seems to have started with his dad, perhaps.
To me, the other thing is that Gatz shows us the list of goals that Gatsby had made as a kid. It seems like Gatsby's goals had been purer at first. But then he met Dan Cody and started to be much greedier.
First, concerning your question about Mr. Gatz in The Great Gatsby, we can't really speak for a writer. We can't read his mind and shouldn't pretend to. That would be sloppy scholarship if I pretended to you that I could do that.
I can, though, tell you what some of the effects are of Fitzgerald having done so.
Mr. Gatz's appearance and presence in the novel adds poignancy (a quality of specialness) to the closing events of the novel. Mr. Gatz is not greedy, and neither is Gatsby. Gatsby's wealth serves the purpose of getting Daisy back--look how he wastes so much money to throw his lavish parties, all in the hope that Daisy might happen to stop by one sometime. And Mr. Gatz's "awed pride" is the pride of a father for a son who has made good. His pride is the pride of a father for a son who has fulfilled the American Dream.
The father's disappointment at the sparse attendance at the funeral adds to Nick's disappointment, as well, and emphasizes the character, or lack of it, on the part of those who certainly do not fail to show up when Gatsby is throwing parties.
In addition to adding poignancy to the concluding events, Mr. Gatz serves other purposes as well. He doesn't reveal where Gatsby gets his greed from, as I've already mentioned, but he does reveal where Gatsby gets his naivete from. Mr. Gatz has clung to Gatsby's childhood list for years, believing it demonstrates a great deal about his character. In reality, the list is likely a typical list children and even early adolescents make--favorite songs, best friends, etc. Notice that nothing is mentioned about how rigidly Gatsby followed the list as a child. (Opinions do differ about the list, though, so I could be wrong about this part.)
In short, Mr. Gatz adds poignancy, reveals a little background while giving a glance at another Midwesterner, and, finally, by the way, gives readers a quote to talk about concerning the novel's title:
"If he'd of lived he'd of been a great man."