I kind of like it in that the BC years stretch kind of indefinitely and most people generally don't have an idea of the date of anything that is BC. This HE calendar gives you a more useful 0 in my opinion. However I'd argue that the creation of some temple which just happens to be the earliest known so far is pretty arbitrary. What if we find a temple that is a few thousand years older do we then throw away all our current dates? Basically it is just problematic to pick an epoch based on something a) the date of which is not accurately defined and b) the significance of which is debatable - there are after all sites of human habitation that are known to be older e.g Theopetra Cave in Greece which is thought to be 130,000 years old.

How about use a more recent and well defined date like the 1969 moon landing as our epoch? I'd argue that is a very significant event in human history when we became no longer bound to the Earth. Or use the Unix operating system epoch of Jan 1st 1970 which would celebrate our movement towards software that is ethereal and could transcend human carbon based existence. And then knowing the date of something to be 12,000 years Before Moon or Before Unix requires little adjustment to figure out how many years ago from today it was.

Unix time also has the massive advantage in that it is widely supported in all programming languages and operating systems although we would need to persuade the ISO folks to agree on a human readable representation that distinguishes Gregorian dates from Unix dates. Eg. use a 'U' instead of 'T' in ISO 8601 date formats so instead of 2020-08-18T16:20:00.0Z for 18th of August 2020 4:20pm in "Zulu" (aka GMT aka UTC) timezone, use 0050-08-18U16:20:00.0Z - oh and we'd have to allow for and get used to negative dates of course. Fortunately negative dates are already supported in ISO 8601 although there's a wrinkle in the 0000 == 1BC because there is no year zero in the Gregorian calendar.

We can't likely set up our own calendar. We can however refrain from historical dates referred to as B.C. (Before Christ) and A.D. (Anno Domini). We can instead use the more secular terms B.C.E. (Before Common Era) and C.E. (Common Era)