Perhaps there was some specific lineage of monks and teachers who traced their founding back to Rahula? If so, they might have had an incentive for concocting a special relationship between Rahula and the Buddha
Another possibility would be that the invention of a son for the Buddha was a way of combating vicious or salacious rumors.
For what it’s worth, in Rahula’s gatha, he says he is the Buddha’s son:
https://suttacentral.net/pi/thag4.8
On the other side of the question, assuming Rahula was the Buddha’s son, the question then becomes why the earliest literature ignores that important fact.
It could be that fact that the Buddha had previously had a wife and son, and had not always lived the holy life, was found embarrassing by the earliest monastic compilers, and that only later did the tradition make its peace with that fact as instructive stories about the Buddha’s family life gradually made their way into the popular lay tradition.
Another possibility would be that Rahula was indeed the Buddha’s son, but was illegitimate, and this was felt to be sufficiently embarrassing that the compilers were discreet about it.
Another possibility is that the Buddha obscured Rahula’s true parentage from his followers, since he wanted Rahula to be treated like any other Bhikkhu, but that the knowledge was preserved though the gatha and the recollections of a few intimate relatives and acquaintances.
On a related question, isn’t there a discourse where the Buddha confronts, or hears the confession of, a man who slept with the Buddha’s (former) wife? Perhaps their was some doubt about Rahula’s true parentage.