Speaking of.. the Amish use scooters fairly extensively, but not typical scooters. Their scooters have very large tires by scooter standards; tires meant for children's bicycles. I think these would be much safer than typical small-tired scooters.
https://duckduckgo.com/?t=ffab&q=amish+scooter&iax=images&ia...
I got the thing because I loved e-scooters so much but I felt like buying an e-scooter was an unacceptable action given how much it would increase my probability of lifechanging injury or death. But ultimately I found myself stopping using it.
Plenty of cities did just that, after a rash of pedestrian (and equestrian) deaths. What resulted was a multi-decade lobbying effort that redefined the "street" to mean a thoroughfare for combustion vehicles.
Plenty of cities are now walking back that effort and are once again banning combustion vehicles in their cores, or at least are not dedicating the space entirely to cars and trucks. A ho-hum example is Kaiserslautern, Germany, where you can drive in the city core, but it's just much more efficient to park in a lot outside the core and walk.
In the process of typing this comment, I discovered that I agree with your overall point, but I would suggest ditching the "protected lane" part and simply take away the dedicated space for cars.
Banning e-scooters wholesale rather than figuring out how they can be part of a safe mobility culture is like banning combustion vehicles at the onset of the invention of cars.
I will agree though that safer electric PEV like e-bike or e-tricycle are likely safer, as are those with speed governors, and add in dedicated protected lanes.