That entirely depends upon how you figure to get rid of religion. Having a society without religion HAS been tried, and more than once. The problem is, every single time it has been tried (that is, religion/belief in deity is outlawed) we end up with genocide that outdoes any death count that can be attributed to any religion.
Every.
Single.
Time.
So from this we can conclude that forcibly getting rid of religion does not make anything better.
What if it just sort of fades away because people lose their belief in a deity? Well....I don't see that it's doing the world a whole heck of a lot of good, myself, but then I, being an uncompromising theist and active member of a specific religion, may be biased.
What I HAVE seen is that if there isn't a religion to help provide societal cohesion and a moral code, said moral code has to come from somewhere else....and that 'somewhere else' tends to be either something one takes out of a religion, or adopts from some humanistic philosophy. As far as I can tell, humanism is just a religion without the name, and 'humanity' is put in place of deity.
Perhaps it would be better to wonder why, if there is no deity, humans keep making one up? Religion has to serve some purpose vital to humanity, or (again, if there is no God) there wouldn't be any.
"Imagine" has a pretty tune, but frankly? It's the dumbest song I have ever heard.
Not the point many people believe that religion causes more problems than it solves. I am asking for people that think that to explain to me why the world would be better. This is a mental exercise.