To promote the incoming anime.
Apparently, Animeism (a late-night Japanese anime programming block on MBS) -- and to the extent of anime produced by MBS -- has a routine of cutting entirely/shortening next episode's previews by 15 seconds to promote incoming anime when it's nearing the end.
In this case, since Kill la Kill's next episode's previews were 15 seconds long, they were entirely cut and replaced by PVs for Riddle Story of the Devil since episode 19 out of 24 (refer to the Wikipedia's list on block B2). Also, since they had worked on next episode's previews, they would be wasted if they hadn't shown them somewhere (e.g. official site).
Another example is Hozuki's Coolheadedness which had 30-seconds next episode's previews. In that case, they're shortened to 15 seconds then continue with Knights of Sidonia's 15-seconds PV.
Lastly, even for non-Animeism anime, but produced by MBS like Magi, it's also affected. Their 15-seconds next episode's previews got entirely cut to show 15-seconds PV for Haikyu!!
previews resumed in the later episodes!
This is just a theory since I don't have enough information to make a conclusion, but if it's not simulcasted or otherwise on streaming sites which had more flexibility in time arrangement, then the next preview could be added manually from the official site.
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