> You want them away from boiling water, dropped knives, and dangerously hot ovens.
This sort of stuff is exactly why the separate kitchen doesn't work at our house. The kids want to be where they can see us, and, with the way our kitchen is set up, there's no way for them to do that without being underfoot. At the same time, we want to be able to keep at least a vague eye on them, and that's not not really possible if they're in a completely separate room.
Versus, when I was little, our house had a kitchen that was separated from the living room by a counter. Which things much easier: We could hang out in sight of Mom, Mom could keep an eyey on us, and we weren't creating a safety hazard (or hassle) just so long as we stayed on one side of the counter.
It's also a total PITA at dinner parties. These aren't the old days, where it was OK for one person (always the same person) to stay isolated in the kitchen for half the evening, and it was understood that it's a private space where guests aren't allowed. Instead we end up with more and more people congregating in the kitchen, socializing with the cook and then with each other, until eventually literally every guest is there, getting in the way of the cooking, and they all have to get kicked out so that we can open the oven safely. Then you're isolated for a little bit, until someone needs to get another beer from the fridge, and ends up staying in the kitchen to chat, and then another, and it slowly ramps up until a mildly dangerous cacophany again. Rinse and repeat until dinner is served.