Some governments do do direct democracy, switzerland has referendums written into their system, as do many US states, over 30 of them, most of which can be citizen initiatives, getting a percent of signatures of registered voters to get an issue on the ballot for a vote, most of which makes constitutional amendments that can't be easily changed by lawmakers, (although they still do ratfuck them before and after the votes.)

It is how we legalized weed.

I don't know the entire list, but there is some direct democracy out there.