I find one button interfaces that trade buttons for time to be confusing and unintuitive. The only way to operate them is by staring at them until they show the desired action. You can't adjust it without looking at it at all (which may or may not be desired depending on the use case). If you happen to miss the target action, you have to wait until the full cycle goes through again. Sometimes they make it so you have to hold down the button to cycle and then release when you see the thing you want--if you miss it, you can't just release and start over, because releasing is going to select the wrong action. This may not be the definition of unintuitive but it is the definition of annoying and inconvenient.

I had a pager back in the 90s that was billed as being easy to use because it only had one button. But it took forever, considering the actual complexity of pagers, to cycle through all the actions--and pagers only have like three actions on them anyway.