Think about your two major target audiences for that franchise. Young kids, and competitive scene Pokefans. The latter is going to tear that game to shreds in a few days (not to mention PVP is gonna be a bloodbath) and how much do you really want the former to be hanging out in an MMO?
Not to mention, I remember Nintendo getting "fox newsed" over fricking Pictochat, not to mention reading sensationalist editorials online about how any adult seen playing Animal Crossing should be treated as a potential child molester. All it's gonna take is one kid giving naively giving out his personal info and the pundits would have the field day of the century.
Balancing a Pokemon MMO would be a logistical nightmare. Hell, it's no small feat under the current model, where GameFreak is already making balance and gameplay changes from generation to the next while maintaining compatibility with the previous generations.
Now imagine a situation where new content is simply added to the world via updates... all the new content needs to be balanced with the old, and players will lose their shit if their monsters get nerfed. Imagine how complicated that gets after only a few updates. In a game that's all about team building, optimal teams will be a matter of course, and no amount of updates will ever keep up with the competitive scene.
Then there's the simple matter of the payment model. How do you monetize a game like this that will be marketed towards kids? You can't do subscriptions, what kind of micro-transaction system to you implement? What do you put behind the pay wall that isn't going to disrupt the already delicate balance?
In short, the idea of a Pokemon MMO only sounds like a good idea if you're of the belief that there's no actual depth to the series. In reality, it would be a herculean undertaking that I wouldn't wish on my worst enemies.