In my experience, the main way it helps is by preparing me for other disturbances (sounds). I think that we're processing sound in a relative way, so if you have silence and all of a sudden there's noise, it will demand attention. By having something in background, I reduce the difference between the current level and the distraction.
The trick is to find the sweet spot. Too loud and it'll be distracting, and in fact even too low is distracting for me, because I attempt to focus on it too much.
Also, nature sounds do seem to have a calming effect, regardless.
[0]: https://mynoise.net
Now I use bluetooth earbuds and put on D&D podcasts, and I'm out in 15 minutes. If I happen to wake in the middle of the night, the podcasts put me to sleep again quickly. My biggest issue now is just not being able to remember where I fell asleep the night before.