Here is a site on how to wash a pillow. It says about what others here have said.
I use solid foam pillows which are even harder to sink, but don’t bunch up. I use towels to sink them too.
They can’t be dried in the dryer, so I put the pillow on two large towels, and roll them up, tightly, to get as much water out as possible. I sometimes have to do this twice to get all the excess water out. Then put them on a sweater rack to finish drying. I also place a fan near by to keep the air circulating.
I think this method would also work on fiber pillows, but not down.
This reminds me that my husband used to have a standard-sized feather/down pillow from when he was a kid. It must have weighed five pounds. I don’t even want to think about what had accumulated in it. It finally got tossed.
I thought I’d update this, as the last of the 8 pillows have gone through the washer and dryer…
The last pair of pillows were a bit of a problem - they’re overpriced Calvin Klein ones ($150 per, on sale, a couple years ago) and I’d rather not throw them out.
The fabric cover on these lets water and air in, but neither out. My front-loading Samsung washer was very unhappy with one of these - the display that counts down the time remaining stuck at 12 minutes for a very long time, while it tried shuffling the pillow around to get a spin that didn’t vibrate too much. It would get up to a reasonable speed and give up, only to try again.
I wound up pausing the cycle, opening the door, and squeezing the pillow by hand (it was completely inflated like a balloon) to force some of the air and water out of it. After a couple rounds of that, the washer was able to complete its cycle, and the pillow came out flat and limp (but the dryer took care of that).