Class 3 eBikes on shared bike paths — where does this community stand?

This came up in a conversation with some non-eBike cyclist friends last weekend and it got heated fast. They feel like 28 mph Class 3 bikes have no business on shared bike paths and should be limited to roads. I think the real issue is rider behavior, not the bike class. But I am curious where this community stands. Should Class 3 eBikes be restricted to roads? And what do you think is the right approach to advocacy — push for more eBike-specific infrastructure, or focus on education and enforcement?