I have experimented with tuning them off and back on. I have found that I use more energy than just leaving them on all the time.
Now we sometimes turn it down a couple degrees the when the boys come back home the will change it a couple degrees this does save some energy.

The reason I went with a 9,000btu split in the bed room is my wife works night shift so that one runs all day.
The hottest days the room would warm up to about 85'F with a 6,000btu window unit.

We have three Gree 9,000 BTU 27 SEER Terra series. They are a great fit for a bedroom.
They will keep it as hot or cool as you want and do the job quietly enough to still sleep.
These all run 24 x 7.

I gave to agree with your points. They are excellent.