Payment services start with an incredibly trivial base requirement: track an integer for every account, let an account decrease its integer and increase the integer for another specified account, and convert between some other payment mechanism and your integer. Sounds like the kind of thing you could put together with a web framework and an afternoon, and then just spend a pile of time and/or money marketing it so people will use it.
Now add the invasive requirements of various governments to track the movement of money (formerly to "fight organized crime and money laundering", later to "combat the funding of terrorism"). All of a sudden an incredibly trivial problem requires piles of lawyers, legal research, logging, information collection from account holders, information verification, responding to "requests" for information, shipping around physical paperwork, and generally dealing with a pile of stuff that should have nothing to do with a payment system.
On top of that, even if you don't want to deal with issues of fraud (hey, cash doesn't), the various other payment services you'll have to deal with to get money into and out of your account still have piles of ways to screw you with it. If you take credit cards, cardholders will do chargebacks to take money back from you. If you take other Internet payment services, you get to deal with the issues raised in this article just like any other merchant. Most people don't want to trust a new payment service with a bank transfer right away. If you accept mailed or scanned checks you'll probably have to deal with check fraud. And without a physical presence and giant piles of extra money you can't convert to and from cash.
Oh, and if you want to make a service as close to cash-equivalent as possible despite all these requirements, then the first time your service transfers money for some notable illegal or questionable operation, you'll probably get shut down over one of the details you missed, which would probably get overlooked if you operated just like every other "financial institution".