i think their concept for Pokemon is that your handheld device is essentially your "real life pokeball" and thus the games work like a "real life MMO"

You walk around in REAL life and meet another person with the game, a trainer if you will, and then battle and/or trade with them.

A console game doesn't capture that essence.   I've been for years wanting and wishing for a MMO pokemon.  Not to long ago I realized that it has always bean an MMO.   Obviously not what MMO stands for in "online" part, but same gist.  

Because children have moved to mobile.

The pokemon games are pretty bare bones. It is all about collecting and leveling up pokemon, but there isnt much of a story. I think nintendo realizes that this dynamic is a better fit for handheld or on the go gaming. Im sure they have probably done research on it in fact.

Nintendo has no say in that matter, the Pokémon Company does. Furthermore, Pokémon has stayed a handheld franchise because of portability (pocket monsters), low development costs, and bigger returns - pretty simple.

They tried? Colosseum and XD. Those sold like 2mil and 1.2 mil. Handhelds sell like 15mil+

More $$ to be made on handhelds, and the Japanese aren't too keen on consoles.
Also, the handheld is a more reliable market as they've ruled it for over 20+ years. They know how these things work. The console markets are based on U.S and Europe, where the market is volatile. It isn't their homeground.

Say what you will, a full HD console MMORPG Pokemon IS NOT HAPPENING. It will not bring as much $$ to the table as a handheld Pokemon game. Period.

Some users have already posted some great answers that mostly answer the question

One thing I'll add though is that a full fledged Pokemon MMO with HD graphics woukd be an absolute flagship title for the Wii U and could push a massive hardware boost. It would also allow Nintendo to send a message that they can compete in the online space.

I doubt it will happen but would love to see it.

Pokemon is like children's Monster Hunter, it's a social game meant to be played on the go, with friends at school or work or other social event. If it isn't readily portable, it can't be readily used in the group, and if you are unfamiliar with Japanese social culture, it's all about groupism.

thank you! this answers the question for me.  I always wondered about that, this makes perfect sense

They want it to stay the killer app for their handhelds. If they put it just as much on home consoles there would be less handhelds sold. It would be a Vita-PS3 scenario. Uncharted on PS3>>>>Uncharted Vita. If Uncharted were only on Vita and had gained its popularity on PSP maybe it would be more of a system seller.

Gamefreak is tripping. I understand that they prefer it on consoles, but they have to know it would help out their parent company a lot.