While it depends on your perspective, I'll contend the Swiss referendum system has also disadvantaged certain groups of people as well. One example of that was the 2009 minaret referendum:
It's an example of using a referendum system to religiously disenfranchise a minority population. Further, much of the imagery used to persuade the population to vote for the referendum, such as the Muslim woman wearing a chador across the backdrop of a Swiss flag covered by minarets that look like missiles, was bigoted and defamatory.
My point in raising this incident is to provide an example that a direct referendum system has advantages and disadvantages. One of the disadvantages seen here is that the system can be used to remove a right from minority population important to their cultural identity. More broadly, there's always a tension between majority rule and protection of minority rights in a democracy and both the California and Swiss referendum systems allow those lines to be redrawn by populist appeal.
Isn't the main problem in ça that there are few limitations on how much can be spent to promote and initiative and essentially buy the result?
And this seems to impact the quality of representative democracy too...