The main obstacle would be that people have, for thousands of years, adopted one thing or another as money. Once the idea of money enters peoples heads, they promptly create money if it is absent. Usually within hours.
As others have explained, money is a valuable tool that serves people well.
You might as well ask if a new society without the ability to write were possible. If such a society suddenly sprang into existence, people would immediately invent a way of writing.