In Berlin, Deutsche Post use electric trikes and mail here is very efficient.
If you look at USPS annual reports to congress they have ~27k motor vehicle accidents a year with a fleet of ~236k vehicles (~216k delivery).[1]
So possibly 10%+ of their vehicles are involved in accidents each year.
If we look at occupant fatality rates for vans (what usps currently use) they're one of the safest vehicle types.[2]
Meanwhile if we look at motorcycles the fatality rate is nearly 10 times higher.[3]
Bicyclist numbers look better at first glance but that's probably because the rate is by total population and not registered vehicles (because you don't have to register a bicycle).[4]
I know in my state (Louisiana), riding a bicycle on a road with other vehicles is considered notoriously unsafe.
Anecdotally I've had friends who reported incidents of people opening doors of moving vehicles to purposefully hit cyclists (and if you search american news media you'll see reports of intentional 'dooring').
[1] https://about.usps.com/what/financials/annual-reports/fy2022...
[2] https://crashstats.nhtsa.dot.gov/Api/Public/Publication/8126...
[3] https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/...
[4] https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/...
You could also ignore vans entirely and look at compact cars (the worst of the passenger vehicles) and it's still a bad look for motorcycles.
I don't know that driver quality really matters here. If you're hit by an SUV or a truck (which is what most americans buy) when you're on a motorcycle it's going to be a worse time than if you're in a vehicle with airbags and crumple zones.
Also don't forget about all the young guys who are riding spiritedly everywhere. Even if you're good the inherent risk of that is high and given enough exposure...
AIUI, the US Post Office does everything in one.