Shenmue III saved the franchise. It is because of Shenmue III that we got Shenmue I and II HD, Shenmue Merch and now the anime, the franchise is alive because of Shenmue III, but if we think about all the problems that happened in the Kickstarter, people feeling betrayed because no Steam version at that time, and all the other things that happened then it did some type of damage.
Some people now even disrepect Yu Suzuki, some people think that the franchise is dead because of Shenmue III as if Shenmue III is the worst game of all time that don't have anything good and much more, i saw this things many times and this is really sad.
About the game... Yu Suzuki said that his score for Shenmue III is 7.5, it is clear to me that he wanted to do more with the game but that he had many problems in the development of the game, it was a kickstarter game, Yu Suzuki is not with SEGA anymore, i really imagine that it was really hard for Yu Suzuki. I really think that the version of the game that Yu Suzuki really wanted to do would have Baisha, but we all know what happened, Baisha is not in the game.
I became a Shenmue fan because of Shenmue III, everything started for me when i saw E3 2015 moment with Yu Suzuki on the stage announcing the Shenmue III Kickstarter.
Before that i wanted to play Shenmue I and II but i didn't had a Dreamcast, i remember even seeing a magazine with Ryo on the cover at that time, i always felt something beautiful about Shenmue even before playing for the first time, i always wanted to play Shenmue but no Dreamcast for me at that time. I remember i even tried to play on the emulator some times.
I think i had problems with the emulator, and was the only way for me at that time so i gave up, but when i saw that beautiful moment of E3 2015 with Yu Suzuki i thought... "that's it, i need to play Shenmue I and II" i played the games on the emulator because was the only way for me at that time, then after i finished Shenmue II i saw the Shenmue Dojo site/forums, now here i am in the Shenmue community.
I love Shenmue III, some things i think could have been better but overall i love the game, Yu Suzuki and the team did everything from scratch with limited budget, what they achieved is beautiful in my opinion, a true Shenmue experience.
So my final answer is... no, Shenmue III did not hurt the franchise, we are even getting an anime, the series is more alive now than it was in the past and this is wonderful. Shenmue III saved the franchise, and i have hope that we will get Shenmue IV and Shenmue V, and this way see the conclusion of this beautiful journey.