EDIT: In practice, larger cities in California seem to have a comparable number of referendums as well. Unfortunately, they're all bundled into an election every 1-2 years rather than the Swiss system of elections every 3-4 months. This has its upsides, mainly in turnout which is still low in much of Switzerland, but also means many "less-notable" issues often aren't discussed in CA to the same degree that they seem to be here.
And of course, CA still has daylight savings time because this proposition required two thirds vote.
Taiwan (the Republic of China) is another jurisdiction with direct democracy elements. Direct democratic rights have been in their constitution since 1940s, but they weren't seriously implemented until 2000s. The exercise of these rights is still relatively new in Taiwan.
As you said overwhelming majority, are there any countries that have direct democracy or come close?