> Normal people don't have the time to vote on every single issue
You could also grant use of your vote to different parties depending on the subject matter, maybe you like Bob to cast votes for you on environmental issues, but prefer Susan to do it if it has to do with foreign policy. Which bucket an issue falls into could be handled similarly, a third-party you op-it to trust to categorize issues before your vote is handed off to other parties that are voting on your behalf.
Those are just some that come to mind, you could do much better. But the point is that with modern technology it would be easy for everyone to choose where they want to side on the direct democracy v.s. representative democracy spectrum, and they could do so on an issue-by-issue basis.
The problem isn't that it's infeasible, it's just that nobody's tried because it would take power away from those that are currently holding it.
This idea is common in a lot of new ideas about representation (eg the German Pirate Party's Liquid Democracy http://liquidfeedback.org/) yet I'd argue it is also a really bad idea.
One of the key values of any democracy, and direct democracy in particular, is that it values and promotes human autonomy. Instead of being subject to arbitrary powers, the 'people' rule themselves - we are only subject to laws that we ourselves have authored (or delegated to others to author in our current cases). But allowing everyone to vote on everything violates autonomy.
Most people recognise that autonomy requires having some/equal say in matters that materially affect them. Yet few realise that giving others a say in matters that don't affect them undermines the autonomy of those affected. So while laws apply relatively equally to all those in a jurisdiction, the distribution of effect is far from equal.
Proxy voting allows those with little skin in the game to drown out those significantly affected by proposed laws. The fact that people don't have the time to vote on every issue, and so will only likely vote on matters important to them, is one of the major strengths of direct democracy.
> Proxy voting allows those with little skin in the
> game to drown out those significantly affected
> by proposed laws.
You'll only get minority issues through if the minority cares enough about it and it doesn't negatively impact everyone else, or if the negative impact from not giving the minority what they want would be greater than just giving them what they want.
I think you'd be more likely to reach a consensus like that using proxy voting than you would be in a direct democracy. With proxy voting any fringe issue will by default go to some general issues political party of your choice, which is likely to have a reasonable position on miscellaneous issues like this.
With direct democracy where 1% really cares about some issue but the 99% doesn't care either way (so much that they can't be bothered to vote either way) you might never end up passing it because you have another 1.5% population of voters that just votes "no" on everything out of general principle.