Out of those you listed the statement is a lie for everything but FF.

CoD was never properly on consoles till this gen, and has been supported on Wii I really don't get that point.

RE4... first on GC... was supposed to stay excusive... need I say more?

Metal Gear originally released on the MSX2, then NES got a really shoddy port, and original games with a lot of work put in them were put on GC and PSP.  Hideo Kojima is pretty good for supporting Sony products other people do his ports... there has yet to be Metal Gear on the DS for example.

GTA goes where they can put it, it was originally a PC game, the game that started 3D GTA was on N64 (pst the losing console)

As for marketing, dev teams, and budgets.... really man?  You're trying to go there?  You realize there has never been a time in the history of game making that it has taken such huge teams to make a single game, and it could be pure rubbish and a lot of the time is, but that's not how it's going to be marketed.  Most of the games that have "effort" put into them is because if they don't make a game look pretty then people will shrug it off, they put a lot of man hours into that, costs them a lot of money, a lot of time, and then to protect that investment publishers HAVE to give it high marketing budgets and even then a lot of games fail to make money...

Honestly here since you want to bring this up tell me previous gen games that HAD the same size dev teams, had the budgets, had the marketing, Shenmue is probably the closest thing... but even it's dwarfed now... which defeats the point all together, since that is not above and beyond effort into a game that's simply what they have to do to get a game to a certain graphical standard and doesn't indicate at all the quality of said product.

But it's not like I don't see what you're doing, you're throwing out a red herring to divert from the fact you have no factual basis for your claim, as franchises, IPs, etc hop around as they please and always have, and usually most IPs die out or start up in one gen.  No one franchise is a good indicator of "big game" because at any moment a "big game" could just drop off the face of the world and it has happened time and time again. 

So really there is no tangible definition of "big game" that isn't in some form rooted in opinion, unless you want to go out, do a proper survey over a period of probably 10 to 20 years to see which games and IPs people will say they know about, think of as big, and still see as a quality series, cause your definition only fits you and some people on the interwebz and even then obviously there are disputes...

I really don't know how you cannot get this.  There is no IP floating around that is in any way shape or form a direct indication of both a "big game" and has always been put on the lead console, NONE, because popularity and standards change constantly and give rise and fall to new IPs, there is no way for your definition to hold water without it being completely your opinion as what *IS* a "big game", period.