To generate power from wind, it is neccessary to sweep large areas. Balloon based systems have been proposed, such as this one:
This is a cylindircal balloon, floating in the air horizontally. It rotates with the wind to gerneate power. The proposed prototype would have been about 30m length 17m diameter for 100 kW electrical power (source). Gross weight would have been about 5.9 t, with about 5.700 m³ Helium to lift the balloon. The company website is down.
A more recent example is this donut-shaped balloon with a fan inside. Currently I find no info on AWE on the companies website.
I'm not a wind power expert but my guess is that a balloon based AWE is harder to scale up to a size where it really sweeps a large area for huge power generation. From this page we can guess that rotor (3 blades) plus gearbox and generator for a 600 kW turbine will weigh about 27 tons, which is probably far more then the plane makani is building (tbf lighter is porbably possible).
AWE needs some flight controls either way (can't have a 5 or 30 tons of power plant crash down in a storm, need to account for gas leaks etc.)
Ultimately I think it's the potential for more power gerneation that trumps concers re. complexity etc.