Inbound video streaming over lightning port accessory I am exploring the feasibility of building an accessory (through MFI) that will feed streaming video that will be rendered by an app resident on the host device.

Looking at some similar products (for example EyeTV Mobile accessory by Elgato -- which is also MFI approved), I can see users reporting that the device does not work for iOS > 9. This is reportedly due to: 


  "[...] latest iOS versions may deactivate Lightning devices depending
  on their use of electricity - this may affect the use of EyeTV Mobile
  despite its MFI certification"


...which looks odd - if anything this would cause termination of the stream due to inactivity rather than causing the app not to work.

Is there any reason why inbound video streaming over the lightning port would not be feasible using the latest iOS releases (11, 12)?
No, there's no such reason. The problem with the EyeTV Mobile has nothing to with the fact that it is streaming video as such. It simply means that limits are applied as to how much electrical power the accessory can consume (i.e. a limit on the numbers of mA that it can draw).