Because yagura is a fodder and there were still 2 other people there that could always break them out so no point. controlling a Jin isn't anything spectacular. Only one random black guy in the manga said jins are immune to genjutsu. For all we know they're only immune to illusions.
Well you say perfect jin, but he clearly wasn't. perfect jin wouldn't be effected by normal genjutsu since they can break out of them. Yagura probably just had the beast subjugated. Like naruto after he won the tug of war with kurama.
^ Wtf. Sasuke and Itachi put each other in genjutsu multiple times. Itachi got Kakashi in the burning paper body, although it was a shadow clone it still worked it just had no effect since it was a shadow clone. This just proves Obito isn't skilled enough to use genjutsu during battle.
OT: Good job. This just further proves Yagura wasn't a perfect jinchuriki as one would've broke it. He was probably like Yugito
We don't know how he controlled yagura. It could have been a combination of mokuton and sharingan genjutsu. It could have required Obito to beat both Yagura and Isobu within an inch of their life. Or it's even possible that Obito was the one who made it seem like yagura was a perfect jinchuriki by controlling isobu with the sharingan.