I did that on a trekking bike (admittedly with one kid). I must be Dutch ;).

Though, if I could go back a few years in time, I would just buy something like an Urban Arrow. We had one last holiday and they are awesome for transporting kids + groceries.

I do that. Two kids, not three. And I appreciate that the bike is light.

It doesn't make much sense, in a way: If I have a trailer and 150-200kg of total weight (and I have as much every couple of weeks), why should 5kg more or less matter? But it matters: The bike feels better when it's not that heavily loaded, ie. most of the time.

What matters most of the time, matters.

Definitely. With a kid on the back a bike has to be sturdy first and foremost. It's not a slow bike, but it has just three speeds (start-from-standing, normal, downhill/wind-in-the-back).