The main argument against direct democracy is 'tyranny of the majority' but this , in this day and age, should be able to be addressed by a suitably written constitution.
While there is reason to assume that most people would rather be left alone to get on with their lives and not have to bother with the minutiae of governance, there are issues that so exercise the people, that they would like their voice, not only to be heard but be acted upon.
To have the people decide on every issue sounds unfeasible and after all, we elect leaders/representatives, to make decisions on out behalf.
The problem is, that once elected, representatives have no need to take any notice of the will of the people.
Furthermore, there is usually no mechanism for finding the 'will of the people'.
There is also the problem of politicians not necessarily being the 'best' of us.
I would prefer what I call 'representative direct democracy', where we select the best of our people to office. When the people can demonstrate an overwhelming majority on an issue, in the order of 67-75%, I believe their representative should be obliged by law, to be advocate of and for , that majority opinion.
This would probably be so rare an event, that the business of governance could continue as normal, while giving the people the power of decision, where they choose to use it.
Sovereignty would be vested in the people.
An ongoing discussion is happening at the website below, where you can find an alternative method of selecting leaders from the widest possible base.