People are different, so it is hard to make some advice that works for everybody. That being said, I totally agree with your conclusion. You do not have to lie still in order to go to sleep, or any other reason. In some sense, if you are in such a situation (being tired, needing to wake up early etc), lying still in the bed is already better than any alternative you can do, eg staying in front of a screen. Sometimes you may sleep. Sometimes you may not sleep. Ime, under this intention, it becomes easier and easier to sleep. Just do not put sleep in your mind as a goal, accept that you may not sleep or you may sleep (even better cultivate being indifferent towards either outcome) and lie still. Personally I have learnt that lying still is more important than eventually sleeping or not. It can even be enjoyable in itself.

Disclaimer: I have only had insomnia episodes that have lasted up to a month or so, so more chronic episodes can be different.