Monitors with video outputs?

[Quartz]

With the popularity of streaming and otherwise recording and displaying your shenanigans, I'm wondering if there are monitors with video outputs or pass-throughs? So the video signal gets captured only after it has been displayed on the monitor, thus eliminating any issue of added latency and simplifying cables. Video capture isn't the only possibility: there's also the copying of the display to a projector for an audience.