mcphage may have meant that it isn't a meaningful date for anybody, because we now know that 1 AD is probably at least several years off from the birth of Jesus Christ.
I always hear people make this claim, but on what evidence do we "know" that? There is no contemporaneous source talking about him while he's alive; the earliest we've got is Mark which was probably written around 60 or 70.
Conversely, I always hear the claim that Jesus was born on 1 AD, but on what evidence do we know that? Some random monks in the dark ages tried to guess so they could make a calendar, and that's the guess they came up with.
While the modern estimate certainly has uncertainty too (how could we ever _know_ such a thing with complete certainty?), there's no way it's _less_ accurate than the original estimate made by some random monk in the middle ages, working with much less data. It does not make sense to privilege that random monk's guesses over today's guesses.
According to Wikipedia, there's two different methods -- written Roman records of Herod as mcphage mentions, or using written Roman records of Pilate's crucifixion and subtracting the claimed age of Jesus at that time. Both methods give years that are in the same ballpark, roughly 4 to 6 BC, which should give confidence that they are close. No method gives an answer of around 1 AD. (Actually, it's pretty impressive that some monks working hundreds of years later in the dark ages are no more than a few years off from today's best estimates)
The Wikipedia page on this topic also mentions trying to work backward from the reference to Jesus being "about 30 years old" during his ministry, which could point to about 1. So really I don't think anyone knows for sure.
Yes, so the point is at best, there's no reason to privilege any particular one of these guesses, whether 4 or 5 or 1 or whatever. We just don't know, ergo the AD/BC date system does _not_ center about a date that has much meaning for anyone, which was the O/P's point
Herod, who according to the bible was king when Jesus was born, died in 4 BC. Whether or not you believe in Jesus, the fact that it didn't happen in 1 AD isn't a controversial fact anywhere.
I went and looked at this on Wikipedia and it seems there is some dispute about Herod's date of death: "Most scholars agree that Herod died in 4 BCE, although a case has also been made that Herod died only in 1BCE.[10][11][12][13][14][15]"
Anyway, this assumes historicity of the accounts saying he was born during the reign of Herod but that's kind of complicated by the Moses imagery; this isn't exactly neutral and unimportant. But I guess that is as good a basis as any to try and determine the real date.