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.