I've been thinking about building a similar system for my home.
I live in a geodesic home and the main floor is almost always at a comfortable temperature but the basement floor is always cold.
Thinking about purchasing some vent booster registers and wiring them in with some ducting in one of the walls to suck the cold air out of the basement and push it up into the main floor or possibly all the way up to the top floor.
I checked AliExpress and there were some sellers there who had what I was looking for in the 40 to $80 range, but I imagine the main cost is going to be dropping 10 to 20 ft of ducting through the walls.
I don't think that one of them by itself will completely solve the problem but I feel like since it would be sucking the coldest air in the entire house and mixing it in with the hottest air in the entire house that it would at least help ameliorate the issues.