The biggest problem is the disenfranchisement of those without access to the internet. Yes, I know that voting in person would still exist, but you're lowering the bar for the wealthy, and making a distinction between classes is bad. You're going to make it so that the bar to voting for the wealthy is taking five minutes whenever you want, whereas the bar for voting when you're not is standing in line for half a day during business hours.

The other problem is the ability to associate votes with an individual. The current notion is that while votes are initially counted electronically, they are counted off of a piece of human-readable paper that the voter can easily read and that can be easily read by other humans in case of a recount. The reason you want people to be able to see their vote is so that they can have that same feeling of trust that the votes that they cast are the votes they intended. However, it also allows people's votes to be verified by third parties, thus creating an avenue for the purchasing of votes. Right now, if someone pays someone else to vote, there is no way to verify what his vote was. But under your system, the vote purchaser could require that the voter show his vote confirmation before getting paid.

Note that the problem you're trying to solve is the same one being brought up with the advent of electronic voting machines. The obvious solution is for the electronic voting machine to produce a human- and machine-readable paper ballot that is then tallied by a different system. You still get the benefits of a simpler UI, but you gain the ability for the voter to verify his vote before it is tallied.