It’s not proven that Julius’ bloodline died out. His legitimate bloodline died out, but there is absolutely no way of knowing whether or not he knocked up a senator’s wife and/or some random British slave girl and through her has millions of living descendants.
Over the course of 2000 years, the amount of surreptitious sex and unofficial adoption that has undoubtedly occurred in every family makes everyone’s official ancestry fiction.
Nowadays we have DNA testing and can prove who is (or isn’t) a child’s father. A large percentage of the suspicions that lead to DNA paternity tests turn out to be well-founded. There is no reason to believe that today’s women are any less faithful to their partners than the women of the past.
It didn’t happen so much at the wealthier end of society, but plenty of men have married single mothers (or “widows”, and occasionally genuine widows with children) and adopted and raised the non-biological child/children as their own, formally or informally. After a generation or two, who remembers that grandpa was adopted? Especially if it was done informally, as these things usually were in non-wealthy families. And especially if there was a hint of bastardy about it.
Orphans were and are routinely brought up by non-related people. If your sister and her husband die in a cholera epidemic but their baby miraculously survives, you take the baby in and raise it as your own. Or your teenage daughter gets knocked up by a passing scoundrel and pops out a baby 9 months later - you raise the child as yours, allowing your daughter to appear a bit more respectable and therefore marriageable. That sort of thing happens all the time, and always has.
It’s usually done legally now, and there’s a paper trail to prove it. But 400 years ago, among farm labourers in a rural community? Generally there is no record at all. So, John Smith is recorded as the son of William Smith, and that’s all we know. Who was his biological father? Maybe William Smith, maybe someone else entirely.
Given human nature, over the course of just a few hundred years there is very little chance that anyone doesn’t have a cuckoo or two in their family tree. Over the course of 2000 years, even if perfect records existed, there is zero chance that they’re a true record of who begat who.