This is pretty close. Some mainline stations with gates (at least, the ones managed by NR) are graded on this by the DfT. They keep an average of time the gates are closed and set targets, which is why staff in some TOCs are working longer hours and are being pushed to keep gates closed as much as possible. As for leaving wide gates open, the gates are individually tracked, but one open doesn't bring down the average as much as a whole gateline.
The policy (for my TOC at least) is that if there aren't the minimum number of staff on a gateline, all gates are set to open.
Exactly this, an operational gateline without any supervision (no staff present, no answer on the video/audio help point) presents a safety hazard and should deserve an email to the relevant TOC.