Well it would not have been a launch game, being on the PS4 it would have taken longer to make and would be coming out next year, which is perfect since Halo 5 is coming out next year and the only franshise that Sony has that can compete with Halo is GT.

Even if it were to come out next year, the install base wouldn't be big enough. You can't compare the existing PS3 users with PS4 users after a year. Only a small percentage would have adopted the new console by then.

Moreover, if Sony delays GT6, it would cost them millions of dollars in additional development costs for a new console, especially since Yamauchi is so obsessed with maximizing his games for the hardware.

A racing game doesn't compete with a shooter. Just because they're both big franchises doesn't mean that they're in competition.

Yeah I don't know why they haven't been advertising it. They need to get on that and soon. If they need proof, GT6 has 54,44d pre-orders as of the newest VGchartz list. GT5 had 200,223 pre-orders the same number of weeks till launch.

This game might sell less than Prologue. That's a scary thought.

It's gonna sell just fine, they've got pretty good marketers in their team.

All games compete with each other, if you released 7 games in a week and they were all different genres its ridiculous to say they are not competing with each other.  People only have a limited amount of cash for video games and can't buy everything.  Your thinking about this wrong, I'm not saying releasing GT6 on PS4 would mean they would make more money, GT games are Sony's biggest system sellers and given the choice to put it on a system that's already out and make some cash (which won't even be much if things keep going like this) or putting it on their next gen console and investing in that console that will be around for many more years the answer is obvious.  Actually if things keep going like this and Sony doesn't advertise the game I think it would sell more on PS4 than on PS3, if it was on PS4 you can bet Sony would be advertising the crap out of it, but since its on PS3 I'm guessing Sony is focusing all their advertising resources to the PS4 this holiday and not gonna bother with the PS3.  

Wrong.

1.) If I were to release a family movie and an R rated movie at the same time, do you think that these movies will take each other's sales? No. They're two different shows that appeal to two different markets. GT is a racing franchise with a very established fan base. Do you think these fans won't buy the game? Halo is a shooter franchise with a very established fan base too. Do you think these fans won't buy the game either? Do you think that the people who own a Playstation console will not buy GT just because of a completely different game on a completely different console? The answer to all these questions is NO.

2.) How many PS4s do you think will be sold by next year? Will it be more than 80 million? Of course not. The PS3 is a much bigger market than the PS4 will ever be in a year or even three. No matter what you do, you can't beat the user base. It's like putting up a Mcdonald's in New York or in Latrobe (PA, population of less than 10k). A bigger market will always yield bigger sales. 

Just saying a bigger install base leads to more sales is not true, there are many other factors such as advertising and hype, both of which would be way more of GT6 was on the PS4.  Using that logic for bigger market = bigger sales then that means that the PS2's top selling games would have destroyed the PS3's since it has double the install base.  With the exception of GTA SA and Vice City the top software sales are pretty much identical.  When the holiday season comes and people are on the fence about getting a X1 or PS4 and they see X1 with Halo 5 and no big system seller with the PS4 the average person will pick up a X1.  The PS4 needs a big system seller to compete and it doesn't have to be an FPS to be competative.  

because Sony aren't going to just rip us off with GT6HD

Because they spent years developing it for the PS3 and the PS3 has a larger userbase?