Long story short, we ended up buying SIM cards from Lebara for Netherlands (1GB for a €20, if I remember right) and from Sunrise for Switzerland (1CHF/day for unlimited Internet, extra for voice and SMS). Lebara gives you credit for the amount you spent on a card (or a refill), Sunrise gives half. Both cards can be refilled on the fly.
"Free WiFi everywhere" is a myth. In not so many places where there is publicly accessible WiFi, they normally require your mobile number to send a text message with access code to (in other words, forget about trying to use WiFi access to bootstrap your Internet, such as find the store to buy the card from, without spending your money at least on SMS). Even then, the "free" access is limited, normally to 30 minutes.
And it is absolutely *not* "everywhere". Especially if you go into rural areas - good chances they won't even accept your credit cards, but that's another story.
It will be a good idea to get a hold of SIM cards *before* you arrive, for the hassle and lost time of your vacation will be worth much more than time spent on investigations.