Actually, my research shows that the 2009 iMac was the last one that offered this functionality, which is described in 2009 as "27-inch models also support input from external DisplayPort sources (adapters sold separately)."
This matches my recollection that my 2008 iMac had this feature, and the one my wife got in 2012 did not.
This is most certainly why video input does not exist. What's ridiculous is they clearly figured it out to support the LG 5K display which is the exact same panel and over TB3 which the iMac fully supports.
More likely Apple dont supply it since it ruins the aesthetic of the back having so many ugly ports. I mean, they've also done questionable things for aesthetic reasons like putting the USB port at the back, the power button at the back, the headphone jack at the back. All these ports need to be facing the user, not behind the screen (I have an iMac 2014, so this is speaking from experience). I honestly believe that an artist determined that iMac cannot be used as external monitor.
Just say "No" to the product. I'm not making the same mistake again.
This matches my recollection that my 2008 iMac had this feature, and the one my wife got in 2012 did not.
2009 Tech Specs: https://support.apple.com/kb/sp696?locale=en_US
2010 Tech Specs: https://support.apple.com/kb/sp588?locale=en_US