Does windmill restart often work for airliner engines?
If the engine isn't damaged, and the restart altitude/speed are followed, the engine should start. Fuel starvation, bird ingestion, etc., do not count.

(YouTube) In-flight shutdown.
In-flight restart is tested as part of the aircraft certification, and it must work. In the link above is a video showing the procedure in a 777F simulator.

Engine Restart Capability - § 25.903 (e).
Tests should be conducted to determine that inflight restarting can be accomplished within the envelope provided. Restarts at the conditions of the critical corners of the envelope and at or near the high altitude extremes of the envelope should be conducted to verify the boundary conditions of the envelope (FAA).


Examples of successful restarts:

On British Airways Flight 9, all four jets on a 747 failed after entering a volcanic ash cloud, all 4 were restarted after exiting the ash cloud. One of the four failed shorty after, but volcanic ash is sticky, the particles are very small, they melt, and they clog moving parts. So three out of four isn't bad at all.

For KLM Flight 867 (a mirror of BA 9) it was four out of four successful restarts.