The problem with windmill starts on a gas turbine is - it requires a fairly high airspeed, as mentioned in this bit on starting aircraft engines.
Typically, the APU, itself a smaller turboshaft engine, has an electric/battery start, while high pressure bleed air from it or another running engine or a ground supply is used to start a main engine.
If your only option is a windmill start, it means you have no bleed air from another running engine, or the APU, as in all of them have failed. Quite probably, you've run out of fuel, so a windmill start is a waste of time. APU's tend to start far more quickly than main engines, so if you don't have the time to start the APU, you probably don't have the altitude to swap for airspeed to try a windmill start.
The last thing you want to do if you're in that shape is lose more altitude than necessary when you have no power, and no other way to restart your engines.
Windmill starts on piston/prop planes in the 1930's and 1940's were performed, usually when the electric starter on one engine of a four engine aircraft had failed while the aircraft was parked. They would take off unladen on three engines, with the fourth prop feathered, and use the airflow to crank that engine to a start, then land and pick up whatever they were carrying and go on their way.
Or, WW2 fighter aircraft would windmill start when the pilot dropped external tanks but forgot to switch fuel supply to the main tanks. They'd just change the fuel settings, nose down and reset prop pitch, and fire the engine back up. In some cases, it was quicker than an electric start, or in the case of naval aircraft that used a high pressure shotgun shell starter, it was the only way to restart the engine in flight.