With all due respect, buying plane tickets and voting are quite different processes; when buying a ticket, everybody has an interest in knowing WHO you are, being able to connect your ticket with your credit card and whatnot.
When you vote, we're very interested in NOT being able to connect you with your vote - heck, in some countries it can even be dangerous if the powers that be find out what you voted. (The results being rigged to ensure they remain in power does not mean there's no interest in finding out who the opposition are!)
Also, we would like to be reasonably sure that you voted as you wished and that you were not under pressure to vote one way or the other; this, too, is much easier to keep under control if you have to go to a dedicated location to vote, rather than just clicking a few buttons on a computer in your home.
And, obviously, we'd like to be reasonably certain that the votes have not been tampered with after they were cast; one of the major benefits of paper ballots is that they do require quite some effort to manipulate after the fact - ballot stuffing is a lot easier if all you have to do is add entries to a database.
My preferred voting mechanism would be a hybrid - you go to a designated voting station, where you find a machine in the booth. The machine lets you choose whatever list or candidate you wish to support, then after you've confirmed your selection, it adds your vote to a tally AND prints a paper receipt, which is then deposited in a ballot box. This receipt shows your choice in plain text.
Now, you have the best of both worlds - the machines can give a (preliminary) result the second the ballot stations close; if anyone wants to contest the vote, there's no need to resort to computer forensics to decide whether the data may have been tampered with - simply count the ballots like we've done for the past few hundred years.