I have childish coworkers running around the office, so I can barely get any work done there and I am constantly interrupted.
I am definitely the "no fun employee".
It got too distracting so management put the kibosh on it after about a month, though.
But back when I worked in a "real" office, I had the exact same situation you just described. It was just as noisy and loud as it is here at home.
In either place, I have to learn how to work with distractions in the background, and learn how to ignore them efficiently. So why not do that at home?
Here, I have an "open door" policy, so that I can help my wife out with any homeschool tasks that might be better suited for me.
It can be challenging sometimes, but it's extremely rewarding.
And I'm just as productive here (if not more productive) than I ever was at a "real" office.
But YMMV.
On the subject, eventually the house's temperature goes to the heights. But I'd never worked so much before and the parenting experience gives a great sense of achievement. It's like a family business with its own departments, and its own kind of clashes.