Benzos are used with Ketamine in anaesthesia to combat "emergent reaction" (to us, that would be K-hole). As with the serotonergic psychedelics, benzos greatly reduce the psychedelic effects of Ketamine. So the "trip" would be pretty mellow.
I have personally take Ketamine + Benzos many times. I do this when I feel like taking ketamine but not experiencing any psychedellia. I also found benzos to be of great value to people with low K tolerance who seem to get a short period (around 30mins) of hyperexcitability at the end of the K trip. Benzos completely negate that.
As for Midazolam, it is not just all of the above, but it is also used purely for its amnesic properties - to make patients forget that they just had their stomach split open and their guts rearanged, for example, which would reduce postoperative stess/PTSD.
Also notices that Tiletamine, a Ketamine analogue and veterinary anaesthetic, is almost always foun in combination with Zelazolam ("Telazol"). I assume it is for similar reasons as the above.
I recall reading several studies in which tested Ketamine for respiratory depression alone and in combination with other depressants, and was found to have negligible effects on such. I can dig them up if anyone is really interested.
The normal benzo + K mix sucks, it's a bit more sedating, but it didn't feel 'dopey' like I hoped, plus for some reason it just makes me wanna compulsively do more and more K when I'm on a benzo as compared to K alone, and it sorta wastes it. But I was hoping midazolam would give it that 'dope' feeling, but I'm scared of ODing.
Benzos help by acting as a muscle relaxant as ketamine on it's own has peripheral sympathetic activity and increases muscle tone - not good for certain types of surgical proceedure. As Jamshyd also said, the benzo/ketamine combination is also used to reduce the incidence and severity of 'emergent reactions', which while wanting to avoid them in clinical settings are the reason that people take it as a psychedelic drug. Without the emergent reaction you'd get none of the amazing 'rebirth' feeling that comes with the re-intergration of all your senses.