> In this case the F–35 has three independent displays that can all redundantly display the same information
This is not true. The standby display is just a tiny artificial horizon by the pilot's right knee, so when HUD and primary display is out, all you're left with is your speed, altitude and attitude. This cannot in any way or form be considered "the same information" as the primary flight display of an F35B, and leaves you without a lot of control.
Whether you can limp along with such backup system depends entirely on what is going on at the time the primary flight displays go dark. In a fighter jet, that display may in some cases just tell you what angle and velocity you are going to die at. Furthermore, in challenging conditions you might have to make a decision very quickly and might not have time tuning yourself into the standby display and its degraded information.
This type of degraded backups exist in many aircrafts - you don't want the pilot of an Airbus you're in to be confronted with the plane dropping to mechanical law, or even direct law if taking off or landing, even if these modes are technically flyable and well documented.