Tackling the privacy focus for GA is great, but they're a good deal of products out there that already fill that niche, not to mention the requirements of the privacy crowd usually being a venture into itself.
If you wanted to make it relatively competitive for marketing, the simplest addition would be adding labelling via regex for referrers.
i.e. - Some users want to be able to group Baidu, Google, DuckDuckGo, into a single bucket for comparison. Some users want to break them down into common market segments by country. "https://www.baidu.com/link?url=FyYbCZqj65Vc7A4XeSNrOcQCS2qFX...
is from your live demo referrers, and makes it difficult to actually assess the amount of traffic from Baidu. Using a regex label means that users can break down traffic from Paid/Organic marketing fairly quickly, and start to build up dashboards they can use.
If you ever extended it to allow multiple labels for each hit, could re-run the regex over past data, and could build reports off it, you'd easily have a benefit over GA that would start to wean the marketing crowd off it.