If by a linear timeline you mean one long chronology, as opposed to the double chronology we current have, which is as you say centred around the birth of Jesus, then there are a few problems that are immediately apparent.

If you count forward, as is currently the case (this year is 2018 and next year will be 2019 and so forth), then you have to grapple with when exactly to mark the ‘beginning’ of time, a question which delves into the debate about what actually constitutes ‘civilisation’ and ‘history’ and is further complicated by the fact that getting exact dates for anything during prehistory is literally impossible. Is year 1 when man discovered fire? If so, when did that happen exactly? And where? Is it when the dinosaurs when extinct? When was that again? The closest we know is 65-66 MILLION years ago. Is it the Big Bang? What exact year did that happen? As you can see, the primary issue is that you will always have a dual chronology. Everything that happened before Year 1 and everything that happened after Year 1 and all the things that might mark the ‘dawn of time’ are so inexact in regards to when they actually happened as to render the whole system of one long timeline unusable.

As for the alternative, counting backwards from the present, we are immediately faced with the one thing that makes such a system unusable: historic dates would change every year. This is less of an issue the when you delve into prehistory, because, as outline above, the timelines are so inexact that, a couple or a hundred or a thousand or a hundred thousand years passing won’t change the dinosaurs from going extinct 65-66 million years before present. Even for early human history this is not a huge problem, again because the timelines are so inexact. However, for more ‘recent’, and by that I essentially mean recorded human history, events, the passing of even a single year will drastically change how every single event is recorded not just within an actual historical chronology, but within the collective consciousness of human society as a whole. When people think of the beginning of the Great War, they think of 1914. When people think of the end of WW2, they think of 1945. When Europeans think of the fall of the Berlin Wall they think of 1989. When South Africans think of the end of apartheid, they think of 1994. When the British think of the Battle of Hastings and the Norman Conquest, they think of 1066. These are all seminal events in history. All countries and cultures have such dates that are remembered and commemorated as important. To mark them with an ever changing date would greatly reduce their continuity within society and culture and thereby deprive them of a large share of rightly justified significance.

As for the current system, there is no doubt that it is Euro-centric in that it is centred around Christ and is used globally as a result of historical European predominance. The transition from Before Christ to Before Common Era is largely an acknowledgement that human history does not revolve around Europe. It may seem like a pretty small and insignificant change, but really, short of developing a globally used alternative (which would be virtually impossible to do because everyone would have an opinion on how, when what and why) there is not much more that can be done. The current dual chronology has the eternal advantage of being the one that is currently in use and as time passes, it will only become more entrenched.