Ever since ASWA mode was added to OP, it was broken because of LowThrottleZeroIntegral clearing Iterm during the zero throttle manoeuvres, resulting in almost total loss of control.
There are two things that need to be addressed here - Iterm must not be cleared during the flight (if ASWA is active), but it also must be cleared before takeoff to stop I from winding up.
Betaflight does it in such way that ASWA (airmode) is not enabled until the throttle reaches configured threshold value for the first time after arming. Only then airmode gets fully activated. In practice, this works well to keep I at zero while waiting before takeoff, yet allows full control in air.