Is it good or bad for the alternative system to be used? With reasons, plus an explanation of how B.C./A.D. dates first came into use.
Personally, I think that it is good that there is an alternative way of saying B.C./A.D, using those terms automatically suggests that you believe that Jesus was born in 1 A.D, which would be problematic if you are not Christian. Referring to the post-ancient world times as “The Common Era” allows you to use dates from thousands of years ago without submitting to Christian beliefs. If I were, for instance, to use the terms B.C. and A.D. when discussing historical events with a group of Hindus, they would likely be offended. Whereas if I were to say “before Common Era”, their feelings would remain intact.
There are other advantages, too. At present, there is great dispute over whether or not the position of the B.C. /A.D. borderline actually relates to the time when Christ was supposedly born. Most of us place the birth at what we now call 1 A.D., but actually it may have occurred as much as ten years before or after that. Obviously, B.C.E. /C.E are based on the Christian year numbering system, but at least it isn’t directly tied to the date on which Mary gave birth. This means that it won’t potentially need adjusting if the evidence that the current religious system is wrong becomes overwhelming. Also, in time Christianity will wither, die and be forgotten like many other religions before it, and the B.C./A.D. dates will become meaningless. At that point, the world will most likely switch to B.C.E. /C.E. dates instead.
Note: The term Anno Domini was invented in 525 C.E. by Dionysius Exigus as a way of dating Easter It was used by Anglo Saxons by 731 C.E., and had become widespread by the 9th century.