Not a nuclear engineer, but we covered this in my third semester of physics at University. The short answer is there isn't any engineering reason why you can't do this. The "real" reason is that there is liability here that nobody knows how to deal with. If the unit became damaged and its shielding failed it could sit there and kill people who came near it for years (for example).

I got to talk to one of the engineers who worked on KRUSTY[1] a 10kW nuclear reactor. This combined with some batteries for peak load could run pretty much any house for a couple of decades. (they talk about several houses in the article but realistically the peak load of a single house when the oven, refrigerator/freezer compressor, and central AC are running is a bit north of 10kW. I would seriously consider a way off grid ranch house if I could have one of these to power it :-)

[1] https://www.popularmechanics.com/space/moon-mars/a20127140/n...

RTGs get hot, that's the point of them, actually. Too hot for use in a small area like your fridge. On a space probe or rover on a cold planet, the waste heat is useful in keeping things somewhat warm. On earth, not so much.

RTGs are also large, too large to power a fridge given the power draw for a fridge. There were microRTGs used in some pacemakers, but the long term safety concerns were never overcome.

The decay rate is high enough that you'd need to augment or refuel your house every handful of years. Halflife of 87 years, 25% energy loss in 40ish, 10% loss in just over a decade, etc.

Also, they've got little plutonium pellets in them, which is both expensive and dangerous.