Why the need for a paper trail?

Why the need for a paper trail?

The problem with computer-based voting is that, without a paper trail that takes the place of the ballot (so the counting of the votes is done with tangible ballots), no one can truly convince anyone (even himself) that the counting of the votes was accurate and reliable. There is nothing to show, nothing tangible to handle.

Why do we need papers or something tangible to convince us of anything? I thought we were hackers, here?

This argument is so often repeated that I keep thinking I must be overlooking something, because it seems so obviously false. I offer you a paper-less, yet verifiable solution. In fact, my solution seems to be much better that paper voting, because only a few selected individuals have access to the paper ballots, so most people can't verify anything. Tell me where I'm wrong.

The solution:

1. The voter comes to the e-voting booth and presents to the machine a token of authorization to vote; this token is consumed or invalidated. The handing out of these tokens is a separate matter not under discussion here.
2. The machine asks the voter to enter any unique identifier, password, PIN, nickname, or whatever. This will serve to identify his vote. At the voter's option, the machine may offer to generate a random identifier for him. The machine will make sure the identifier is unique at least within the voting district. The voter will make sure to not tell the identifier to anyone (the on-screen instructions should advice him to this).
3. The machine lets the voter choose his preferred candidate(s), or whatever is the matter of the election or vote.
4. The machine stores in a database a tuple of the identifier and the ballot. After making sure the entry is permanently stored, it thanks the voter and indicates that the vote is done.
5. The voter goes home. He fires up his web browser and surfs to the election's home page. He enters his chosen (or generated), secret identifier, and the server responds by showing his ballot. Thus, the voter has verified that his vote has been registered correctly - something he isn't able to do right now, even with paper ballots or paper trails. Furthermore, they can do this verification instantly, without even waiting for the elections to close.
6. Once the elections have closed, the voter surfs to the election's home page again and clicks on a link for his (or any other) district's complete results listing. The server responds by giving a listing of potentially thousands of identifier-ballot pairs. These are public, because there is no reason for them to be secret. They can be published in newspapers for the benefit of the internet-impaired. Anyone can verify that their ballot was registered. Anyone can verify that there weren't more votes than eligible voters. Anyone can make a recount in the comfort of their homes, and compare his results to the official numbers. All these things are impossible right now, even with a paper ballot or a paper trail.
7. Every voter's privacy is preserved, assuming that they keep their ID's secret (remember, they can choose their own) and that there is no way to connect the tokens (see 1.) to the ballots.

What have I missed?