There are three problems with the proposal, as I see it.
The first: the precise dating of the event being used as the basis for Year 1 is as yet up for debate. What if, in two hundred years time, we have an extremely precise date for the foundation of Gobekli Tepe, and it turns out to be actually 11,089 BC? We'd have created a calendar even more "inaccurate" and meaningless as the AD calendar it's supposed to replace. Further, what if in two hundred years time, we find more, even older, cities? Again, we've rendered the basis for our entire calendar meaningless.
The second: your solution to the current imprecision in our knowledge - by simply adding exactly 10000 to the current AD date - does not truly get away from the "AD problem". It is
still, fundamentally, linked to the AD calendar. I can't see Jews or Muslims being fooled by what would surely seem to them to be a weak attempt at "covering up" the link to the AD calendar.
Third: one could argue that using a single, very specific fact from a single, very specific branch of human knowledge, is
still a somewhat parochial view on what is "the most important event in
history", upon which the calendar should be centred. An archaeologist might well think the oldest piece of archaeology is important. An astronomer, on the other hand, would think that the oldest known astronomical observations might be important. An art historian would think that the oldest known piece of art would be important. A modern historian might consider the launch of the first satellite, or the detonation of the first nuclear weapon, as worthy candidates for a new Year Zero. No-one can agree which of these dates might be actually more meaningful or significant, in the grand scheme of things.
Many other "alternate calendars" already exist and are used daily, in their own parochial spheres of interest. Observational astronomers, for example, already have and use their own concept of an "independent" calendar: the "Julian date" (not to be confused with the Julian Calendar) which recognizes Day 1 as January 1st, 4713 BC, a date somewhat arbitrarily chosen as being the last confluence of three astronomical cycles, and as being (hopefully) a date older than any possible surviving astronomical observation records - so they'd never have to refer to negative dates. The current Julian Day is 2,457,731.
Finally, to address the argument that using a Christian-derived calendar somehow imposes, elevates or legitimizes Christianity above all other religions and worldviews in a society that uses it: I would just point out that the names of our months are not Christian-derived, but rather, originate from the ancient pagan-derived
Roman calendar. Does calling the first month of our year "January" legitimize the belief in and worship of
Janus? Does using a calendar where the seventh month is named "July" imply that you agree with the deification of
Julius Caesar? I doubt most of the people who use the English-language AD calendar in their daily lives are even aware of these derivations.
