My monitor AW2432DWF does allow you to turn off HDR, although it is a relatively recent monitor and my first HDR one, so I don't know how common that is.
HDR for the most part, is a two way feature. must be enabled by driver/de as well as enabled on the monitor for it to in work, because its not always ideal to have local dimming enabled on monitor (one of the key components required for HDR)