EDIT: Early Modernity began around 1500 and Late Modernity (allegedly) ended in 1989. I think Postmodernity still has a few years left to play out.
Moreover, even our calendar and epoch has changed. Since Jesus pbuh was conceived nine months before he was born, the English used to record the beginning of the year as the 25th March OS before they adopted the Gregorian calendar. Therefore, the 20 March and the 30 March of the same year would have different numbers. (The general public still celebrate new years on the 1 January in this period, which can make dates between new years and lady day ambiguous.)
So unless you circuitously define a "calendar year" to mean "the calendar used for measuring compared to C", your statement is false. If you circuitously define it, it is a useless statement which says nothing more than "true statements which can be made about calendar length are true", which is unnecessarily specific while being at the same time redundant.
I thought he was conceived 4-5 years before he was born, if you're going to nitpick.
Also, the radiocarbon dating itself (and thus the beginning of effective absolute dating) was invented around 1950, and nuclear weapon tests made everything after that point unsuitable for the radiocarbon dating. It would be natural to have that point as a reference for the "present" at least for now.
The calibration is there because the global 14C/12C ratio is not constant over the time, and the same procedure can be used given the recent history of ratios (that we do have). As far as I know, though, resulting error bars might be much larger than usual because the function from uncalibrated ("14C") years to calendar years is no more regular. For example see [1] where uncalibrated t2 and t3 can correspond to much larger periods than t1's; historically this happened only locally, but after 1950 it would be far more common. Still the radiocarbon dating can be used with this caveat [2].
[1] https://commons.wikimedia.org/wiki/File:Variations_in_calibr...
That way we can have another shot at it being 1957.