I don't see it as necessarily replacing representative democracy, but complimenting it, giving people more of a say in how things are done on top of traditional voting. If I could explicitly choose how even 5% of my taxes were spent, that would give me a very tangible feeling of influence that I just don't get from voting, at least at the higher levels of government (as an american). It would also push me to do my homework about issues a lot more, but that might not translate to the public at large.
Agreed about the potential for the system to be hacked by powerful entities though, perhaps even worse than it is now...tough to get around that one.
The closest you have to that is making charity donations and offsetting that against tax. In that case you are diverting money away from central government and putting it elsewhere.
Many government projects require a certain level of investment over a number of years or even decades. It wouldn't be efficient to start say a fighter jet development program if you might have to ditch it half way through because public opinion changed.
True, it wouldn't apply well in all situations, but if you tweak the percentages correctly, only giving the people X% of control over their taxes (maybe relative to some metric like income or education), then maybe the government could have enough of a buffer to protect against swings in public opinion for sensitive or critical projects.
But your point about the fighter jet program could actually be an argument for this type of direct democracy. Let's say the public found out that the program was causing, or somehow will cause, the deaths of thousands of innocent people in a third world country. The military could then face spending cuts, directly dictated by the people, that would threaten the program, and rightly so.
That would last until the first terrorist attack or economic crisis and then tend towards 0, because "we really need this money".
Besides you would probably be able to work around this with creative accounting. Let's say everyone wants to defund the military and put more funds into education; military training establishments now show up on the budget as "defence studies schools" because they are issuing general educational certificates to soldiers.
I think fundamentally if you think some particular government is going to just waste large amounts of tax money you should really just not vote for them. You vote in a government because you want them to make sensible choices in how to allocate resources for public projects so you can concentrate on your startup or whatever.
Sometimes this stuff can work on a local level. For example schools can have governing bodies of volunteers (usually parents) who get some say over how the school budget is used.
Agreed about the potential for the system to be hacked by powerful entities though, perhaps even worse than it is now...tough to get around that one.