Well first off, this is Game Freak we're dealing with here, Zero, not Nintendo. Nintendo spin-offs can most definitely be supported (as you even pointed at with Paper Mario). You mean Game Freak spin-offs. Nintendo only publishes Pokemon games; they have no real hand in development. It's not Nintendo's lack of effort, it's Game Freak's. It's not Nintendo's writers, it's Game Freak's.
Anyhow, I agree with you to some extent; they most certainly didn't put much effort into PBR. I honestly think PBR had a bad production deadline or something along those lines. The trailers for it originally showed many interesting features like battles actually affecting the battlefield. Of course, something like that would be a huge project to integrate into the game, given all the moves and Pokemon there are possible that have to be accounted for, so it's almost understandable. Still, the lack of effort and thought is pretty evident.
I disagree with you about the purpose of the game though. Sure Pokemon as we know it is about battling and training with friends and such, but if one wants to tell a story or change the gameplay concept, why shouldn't a spin-off be able to do that? Granted, they may not have done such a great job at it in the past, but I don't think the effort itself is a negative thing just because the main series Pokemon is about training and battling and social stuff. Like you said with Mario spin-offs - main series Mario (as close as you can argueably get) is 2D and 3D platformers (as in 2D Super Mario Bros-esque and 3D Super Mario Galaxy-esque). But they branch off all the time to deliver vastly different spin-offs. Sure these spin-offs are well thought out and made with heart whereas as most of the Pokemon spin-offs aren't (barring PMD of course), but the effort in making the spin-off certainly isn't bad itself just because the main games have a different focus.
But you thought PMD was a failed attempt at bringing Pokemon to another genre? If anything, I'd argue that Pokemon was a seamless match for MD gameplay. Plus, the stories (PMD2/3 in particular) were actually very well thought out and expertly delivered, at least compared to the main series games and other spin-offs.
By the way, you only nagged about XD and PBR. Might you have positive feelings for Colosseum? Personally, I thought it was well done, but the other two I'd have to agree with you for the most about.
And what? The PSP doesn't even have the power of the Gamecube :s