Yes, I do. For the reasons you've already mentioned, it would be a good idea. By and large, the power on the part of people to initiate something under the public agenda takes place through their elected representatives and the political parties, but not always.
In other jurisdictions, where the right of initiative was available, important changes have been made. In Italy, for example, where the Roman Catholic church has a certain position on the issue of abortion, and the mainline parties agree with that way of seeing the issue, it was only because of the right of initiative that women in Italy were able to bring about a ballot question to deal with the abortion issue.
In the state of California, where all the parkland, that beautiful, irreplaceable Pacific Rim, was succumbing to developer after developer, neither the Republicans nor the Democrats at the state level were doing anything, because both were receiving substantial campaign contributions from the developers. It was environmental and naturalist groups that moved to protect this heritage. They forced a ballot question that created the great Pacific Rim national park in California.
These are instances in which the political parties serve as a checkpoint for what citizens themselves might feel. The citizens aren't dictating; they are only triggering a mechanism whereby the issue can get ventilated. Then all citizens have an opportunity to vote and choose a course.