I had a bakfiets, with just 2 wheels. It was easy to ride, the girls both loved it, and it made short trips like our school run easy, quick and fun. Not possible if you have to go uphill much at all, and yes, you then either leave it at the school, ride it home and take the tube/bus/car/usual route to work, or ride it to work. Riding it to work is fine if you can, as the 2-wheeler is more navigable, easy to ride without a load (ie DC in it), less of a block to traffic etc than the trikes, but not everyone lives close enough to cycle to work. I took my girls about 8km on quiet streets, and along parks, so I wasn't too worried about exhaust height; very rarely were we actually parked behind a running vehicle for long. Now I've sold it as we walk to school and I don't need it to cycle with DD2, who has a standard seat.
The main problem: they cost more than a second hand car, or a vacation for 4 (or 2 or 3 vacations depending where you go :) ). New, they are about 1700£ or more! The trikes aren't cheap either. And you have to store it somewhere. Having to get it out awkwardly can make it not worth it, time-wise, compared to walking. You'd have to store it at work or the school, too, and it's so expensive that you don't want to leave it out...