They ALL needed the connection to antiquity in order to seem legit, no matter how cobbled together and contrived.
This is most obvious between the 'old' and 'new' testaments. The writers of the new testament seem to be distancing itself quite a lot from the ways and tone of the old testament, reinventing god from his smiting and angry and impatient old ways to this tolerant and meek and mild way of the son, and while at the same time, not wanting to seem like a completely 'new' god but rather just the older god with a new attitude. 'I have not come to abolish the law, but to fulfill it', and all that business.
The writers of the new testament are clearly trying to appeal to and make-use of this connection to antiquity, as a stepping-stone. This connection to antiquity is why the Catholic church advocated tolerance of Jews and even protected them during the Middle Ages when a lot of Christians would have preferred to exterminate Jews for denying the divinity of Jesus as the lord savior. Jews (and the Hebrew Bible) were the 'legitimizing' link and witness to antiquity for Christianity and the new testament.
Rinse and repeat for Islam. They couldn't just drop a completely new religion, new holy book, and god out of thin air, so they fashioned it as a sort of 'third' covenant of the same god, even anointing many of the same figures as prophets (Jesus, Noah, Moses, Abraham, etc).