I can summarize what I have read on feedhorns. The 40mm barrel style lnb like the MK1 has an integrated feedhorn. Most of feedhorns you see have two issues. 1 they are designed as C band waveguides to columnate the signal mostly from badly formed (out of focus) dishes. 2 they are designed to mount on a lnb that is bolted to C120 waveguide.
They perform two functions on ku band: 1 rain/snow shield 2. attenuate side interfering signals. And obviously the all plastic ones can only do the weather protection. There is no way tune the concentric waveguide for all the c - band and ku - band frequencies.
Here is an interesting link on various dish/feedhorn/lnb questions:
Most important is the size of the area collecting the signal, so if we could gather more signal – better. However, a feedhorn must be directing the signal to the sensor element either by geometry (like a reflector) or using multiple paths (like the concentric waveguide).
Updated after @syed comment: Good note that just a stronger signal is not always better (hence the importance of snr). So. good idea to come up with some shield for noise sources that are not entering the front of the detector.