I'm going to come up with a couple of plausible scenarios where it might make sense to have a robot maintain a heads up display.

In humans, electrical signals from different stimuli travel at different speeds to the brain. From _[Speed of processing in the human visual system](https://link.springer.com/article/10.3758/s13414-013-0436-y)_:

> Here we use a go/no-go categorization task in which subjects have to decide whether a previously unseen photograph, flashed on for just 20 ms, contains an animal. ERP analysis revealed a frontal negativity specific to no-go trials that develops roughly 150 ms after stimulus onset. We conclude that the visual processing needed to perform this highly demanding task can be achieved in under 150 ms.

_Seeing_ and then _comprehending_ something takes a certain amount of time. It is plausible that, due to the design of your robot's brain, the visual comprehension for some specific data points is _faster_ than looking up those data points from whatever memory module they currently reside in. In this case, providing critical data in visual form to the robot would make the most sense.

You can also argue that, during the normal course of operation visually interpreting that data could be slightly slower, but during "stressful" situations _not_ taking the few cycles or so to have to interrogate critical subsystems on their current status and instead rely on those systems to report their data directly to the visual cortex can outweigh a minor loss in performance. The HUD can also be just a backup data view for those times when both the front-side and back-side buses are currently overwhelmed with commands to terminate the local population of organics.

Slightly akin to Pavel Janicek's answer, the HUD stays around for logging purposes. It is possible that the visual link is shared with an upstream monitor that does not have access to the the robot's hardware, just the visual data stream. By maintaining a HUD, this stream will relay valuable information back to the robot's command and control even in the event the silly humans manage to resist termination and destroy the robot. Seek and destroy drones can be dispatched back to the robot's last known position with the robot's last transmitted images.