VAT and EU is complex relationship.

At the moment, when one partner to a trade does not have a VAT number, VAT is charged at the rate of the destination country. It used to be the other way round (VAT charged based on originator country). The EU is a customs union, so nothing exciting here.

VAT, customs and Switzerland is simple - Switzerland is a non-member country, so every export into Switzerland up to the border is, in principle, without any VAT and customs charges. At the border "someone" will have to do these declarations, and just behind that border fence normal delivery ensues. For smooth cross-border trade for consumers VAT and customs declaration services are a massive simplification as they put the effort into the hands of those who are best qualified and make the whole routine very predictable for pricing (e.g. delivery of furniture across the border, to not use online sales as an example, for once)