As I said before, there was barely a hardcore audience at the time the first Mario was out. Mario is a casual mascot, aimed to suck casuals and children into the realm of videogames (IE: Like they did with me). He is put in cartoons, books as a image of what Nintendo has to offer. Mario titles are well crafted, but they are created to generated new gamers and also hold onto the attention of those who have grown with Mario. When I say a hardcore following, I am stating that the brand has loyalists, who find quality in the product and will play it in a more challenging manner than say casuals who will just play from beginning to end. These loyalists will find all the secret rooms and all that the game has to offer. Casuals....do not care to do type of thing. Final Fantasy is a JRPG, which takes strategy. You need to put things into their proper categories. When you say casual...you think anything that is popular. No! Stop that. A casual title, is a 'pick up and play' game that is crafted intentionally to catch the eye of non-gamers. A game that can be played within an instant without having to learn sixteen to eighteen buttons and you can be on your way to having fun. It doesn't provide and intermediate challenge, unless one seeks to progress or one cares to see all there is to see in that game.
Ok, so you can say Mario games happen to be easier to pick up and play than some other titles, fair enough. As you said though, Mario titles hold onto the attention of those that 'grew up' with Mario (i am guilty), but they are created to generated new gamers, this doesn't however make Mario any less core than other game series, it just means Mario also happens to appeal to others. Mario titles still provide the essential material that the core want and expect in the games, you can't use the fact that Mario appeals to a broader audience as an excuse as to why he is not core.
I agree with your definition of a casual game, however a lot more titles fall into this category than you make out. Final Fantasy is a primarily turn based, RPG series, and GTA is a sandbox game. These are not auto handicaps for them to be more core than other genre's (IE, Mario's primarily platform games). Granted, they're maybe not as simple to pick it up and just play it (though i could argue against that), but it's not hard to get the hang of. Renowned and popular franchises can be called casual, if they're selling extremely well, they obviously appeal to a wide variety of people, or the casuals should we say; you cannot insinuate that the popularity of certain franchises are totally core centric because they aren't as easy to pick up and play as some others, you can't say GTA and FF do not appeal to casual crowds but Mario somehow does.
The PSP is more hardcore than the DS, because it doesn't have too many games that appeal to casuals. It has the gorier, grittier, mature titles. It has intermediate level games or higher at best with few casual titles. The DS is a great portable that has way more games that casuals can "pick up and play" along with games that hardcore can play as well. Except on the flip side, theres less of a percentage of hardcore games on that portable. As one person said before...for every hardcore game, there are five casual games on the DS. Nintendo has always thought of everyone and not just the hardcore. This is what everyone seems to forget.
No. For the first sentence, the PSP having less casual appealing games does not make it more hardcore, it makes it less casual. The DS has more casual titles for sure, however that doesn't blight the fact that it also has a gigantic offering of core games as well, just as many as the PSP. Admittedly these aren't as gorier or "mature" (as you say) as most of the core games on the PSP, but this does not make the games any less valid or hardcore.
Nintendo has always focused on everyone like you said, but that doesn't automatically mean they don't think of or provide core games. The casual to core game ratio for the Wii and DS is very questionable, but if people would use common sense and just look, they will find those hardcore games that haters and idiots like to claim are so non-existent. It's just like when people were hating on the PS1/X and PS2 for having so many casual games, they had core games as well, and the amount of casual games do not disregard or bane this fact.