GT5 was absolutely a disaster...but that also rests partly on the shoulders of Sony for their hardware choices with PS3, and their likely insistence on 3D functionality to push TV sales.
It's pretty likely that GT6 was pumped out to the larger PS3 userbase in order to make back some money from GT5 and push some funds to their PS4 project (now GT Sport). That absolutely made sense, considering the wreck GT5 was. GTS has some strange design choices, but none of them really seem that crazy. From the start they made it explicitly clear what they wanted to do with the game, and that was build an "eSport" caliber racing title with a strong online community. Online only makes sense in that regard, as it places fans in a real competitive space as opposed to offline interactions.
I don't think there is mismanagement with the GT franchise as much as their is fatigue for the franchise, and past fans having been burned on GT5. The studio is obviously going through some growing pains with GTS, but with their efforts since launch, it's clear to see that this is one of the best entires into the series since it's inception, and offers a lot of long requested fan features that are improving little by little with every update, along side new free content.
The hate is just bewildering and seems almost childish. It's okay to not like it or be fond of it, but the people that come out of the woods to really blast it is just so weird to me.