Why not just classify them as mopeds? Mopeds have been around for ages, started out as motorized bicycles, are limited to around 28mph, and have standard age, and license requirements. You have to get a license, and plates. I think there is an insurance requirement also.
I feel like applying all the same guidelines to e-bikes would go a long way to resolve the chaos they have been causing.
Obviously there would need to be some new parameters around what exactly qualifies and all that.