It is possible to get everywhere using public transport in the Netherlands, but the time difference is huge. If I use public transport to get to my girlfriends parents house it takes 60 to 90 minutes, if I go by car it takes 30 to 40 minutes.
I vastly prefer a longer ride in which I have my hands free and can do a little work or read a book, versus being chained to the steering wheel in a car. To each his own, of course.
Okay, I guess I was talking more about "viable" than "possible". Or maybe, it should be viable for 80% of all trips and at least possible for the remaining 20%. I guess you can't realise it for all of them, that's just a consequence of urban sprawl.
What's more, for a country the size and density of the Netherlands, anybody should be able to visit their Grandma using public transportation (buses, too, not just trains). I'm not saying it's possible right now, but it ought to be.