You don't need planning for domestic turbines specifically but at the moment the legislation makes it highly unlikely your house will meet the requirements unless its fairly uniquely situated.
The turbine cannot be within (I want to say 5m but its a while since I read the legislation) of a boundary, so for example my house if I was to put a turbine when I would logically do so, on my south facing wall it would be within 5m of a boundary, even though its around 10m from the nearest house.
Its the same issue with heat exchangers as well, the legislation was written when this stuff was unusual, now its becoming far more normal its a problem.
When I walk to the allotment I see houses with AC installed thats technically against the legislation but in modern housing its very hard to avoid that.
As said above the actual generation vs the boiler plate rating is well down. Thats not a problem as such but it can be very misleading as you only going to get close to the boiler plate reading if your very lucky and its only going to be occasional.
Wind is 100% not going to power your house, what wind will be great for is providing a smaller top up to batteries.
Eg trickling in 150w average for a day isn't an inconsiderable 3.6kWh over 24 hours.
The smaller house type designs are far less like the large turbines you see as houses tend to be in disrupted airflow so the designs are more like a spiral.
To me wind is more like solar from the 80s, it needs some massive effort and some decent advances. It needs to become more cost effective and it needs to be accepted as viable and not having to be basically out of sight from the boundary.