Why do you think that similar law could not be passed without direct vote? The problem is not direct democracy but the fact that it is being done in a wrong way.
Voting should be done without anonymity, online. One should be able to either vote for everything manually, or delegate the vote to any other person.
If some change is supported by 100% of the voters it should be implemented immediately. But if smaller percent supports the change, then there needs to be a vesting time (e.g. 10 years for 60%, infinity for 50%+1).
This allows people to either trade support for policies (i'll vote yes for your initiative if you vote for mine, or give me money), or to get high level of support locally and try out various laws on local level.
The same site that manages voting should also show detailed budget of city/state/country, where people can see where their taxes are being spent and should be able to redirect the money they have paid.
Dumbest idea ever.
Billionaire goes: get $10 off at my store, called Scamazon, for these votes (lists votes). And naturally even the $10 is manipulated to be recouped with dynamic pricing.
What we have now is a politician saying vote for me and i'll pass laws that will give you 10k in next 4 years, people vote for the politician who then takes money from scamazon gives 10 to voters and takes 10mln to get elected again.
Eliminating the middleman makes things better already.
But more importantly with vesting time, large number of votes, ease of reversing a decision in a new vote, take $10 and vote for something that costs you more simply won't work.