Most people don't even understand what a SIM is, let alone how to replace one. They probably can find their Settings app though.
I guess to people from the US this may seem "foreign", but it's really simple and it really works.
In America, competition/free market was the priority so the result was many non-compatible digital protocols (CDMA/TDMA/Nextel/GSM). In the US, if you're switching carriers, you are probably throwing away your phone and getting a new (subsidized) one from your new carrier. Even if you are moving from a GSM to another GSM carrier, because of the subsidies the old SIM is probably locked to your old carrier and it might be cheaper to get a new, subsidized one anyway.
Phones here are not appliances that you buy from the carrier. The device and the service are properly decoupled enough that people know the difference.
If you buy the phone and SIM on the carries website, you don't get the SIM and phone in separate packages, so again who would insert the SIM if not the customer?
Changing carries from the settings app would most likely be more confusing. I think some people would be worried if the see the logo of a carrier other than their own in the settings menu.