I think no, because removing real money is not a good idea. Most of the services need a paper money, it will do harm more than good
Actually you cant just give a no or yes for this question. Reason is, there are different aspects and we have to cater everything when we are answering go a yes or no. cashless society can be profitable and it can be harmful. Depends on the item and country in which it is happening. But there will be a time, may be after a century, but it comes when cashless society can be seen.