The system works perfectly for people living there: those who want to keep their own car can get a relatively cheap parking permit, and most only use their car for exactly those rare scenarios you've described. It takes 10 minutes to get to the highway. Nobody is complaining, having a car is simply pointless 95% of the time.
It's a very simple solution and it works.
You have to wait years for a parking permit. And when you want to park your car you have to drive around minutes before you will find a place to park.
I have a bike. It lets me go almost anywhere in Amsterdam, cheaper, more easily, and generally faster than any other mode of transportation. Sometimes you get a bit wet.
There are a few distances inside the city which are not handy. For those I use the wonderful tram/bus/metro network.
Occasionally I'm lazy and don't want to bike, or need to go somewhere strange. Then I grab a car2go (electric smart car, €.30/min, including electricity, insurance, parking anywhere). When I get to my destination I park it anywhere and end the rental.
Since moving here, my transportation costs have gone from many-hundreds-of-dollars per month for a car/gas/insurance/repairs/tolls/parking/fines in the US, to around €40 month for a bike, public transport usage, and short-term car rentals.
It is much cheaper, and much more convenient, to call a taxi or rent a van when the above options don't fulfill my transportation needs.
Travelling from Amsterdam to places without a train station kinda sucks. In some cases, even travelling to places _with_ a train station takes almost twice as long by public transport.
And while waiting for a permit (about 2-3 years, but we live in the area with the longest waiting lists) we could park the care somewhere within a 10-15 minute tram/bike ride. Which is not a big deal if you use the car about once a month. Neither is taking 5 minutes to find a parking spot.
All of these are a small price to pay for the convenience of not needing a car 99% of the time.
Parking is not that big an issue in Amsterdam in general compared to many other major cities. Largely because few people are stupid enough to use a car when a bike or public transport will do...