I sleep without a pillow and have for years. It can be done.
Before going pillowless, I had a buckwheat pillow. It is less cushy and fluffy than standard Western pillows. I believe they are typical in Japan and not hard to find these days. It helped wean me off the giant fluffy Western pillows.
I have respiratory problems. I sleep better without breathing in allergens and dust mites and god knows what from a pillow. Though it did take a bit of time to get used to doing it differently from how I had my whole life.