Hmm no,

• first oft all: noise. Wind turbines have moving parts, that attached to a building or even worse attached to a balcony creates noise in the whole building. Imagine the rattling of 5-6 ~10 year old, bad maintained, wind turbines.
• Second: the energy output is rather low. A 1,2KW turbine is about 1.2m/3.9feet big. That's in spherical, cause it has to be able to rotate by wind direction.
• Third: balconies are preferred to not have wind, but sun.
• And last but not least: blades. Every windturbine form factor has (fast) moving blades. If it's reachable someone is going to stick a finger in it.

If you're living more suburban and have a windy detached place to setup a small windturbine that's an option. On the garage or shed for example.

Sadly really small wind turbines are really ineffective and not worth the investment until you have a really windy balcony. If you only have a few square meters solar is the only choice.

But I'd still love to have a small windmill in my garden.

If everyone puts wind turbines on the balconies they might end up blowing the building over

Doubt it. Wind around buildings tends to be shit.

There's a reason they build turbines on hilltops and out at sea.