The most obvious gap for a traveler is that the EEA mobile roaming price regulation doesn't apply if you are on an EEA operator and roam to Switzerland.
Could be that Swiss customs takes ages to clear parcels. Could be that tax or import duties are complicated or simply just so high that it's not worth it. I knew a lot of people in Switzerland near the German border used to go shopping in Germany because was significantly cheaper, probably still the case today.
The most probable reason why you can't get packages from EU Amazon to Switzerland is because they are not in EU.
The same reason applies to why you can't get packages to EU if you're trying to get them from US.
Yes, some big sellers don't mind but small ones do, and EU Amazon does have a huge variety of sellers.
For example, I've lived in Croatia before and after EU membership. The Amazon situation changed completely and now I can get packages from any EU Amazon.
In contrast, most non-EU stores (except Amazon again) happily ship here, even if the shipping fees may be extremely high and border control is left to buyer's problem.
I usually just search for "Amazon Prime" items, but sometimes those items can't be shipped or aren't even available with Amazon prime! It's a total mess.
- searching for something
- selecting the most applicable category on the left, next to the results
- selecting Amazon.(de|fr|it|es|co.uk) on the bottom left (under Seller)
What is sold by Amazon generally gets shipped anywhere (within Europe?).
As a company, before Amazon Business, this also made sure you'd be able to shop without VAT.