There are several problems with this.
First, there's no consistency in this design. They're cramming everything from the wizard to the warlock to the psion to the artificer under the mage, but make barbarians, paladins, rangers, druids, and bards their own classes? That is just.. bizarre. There's less difference between a fighter and a barbarian than there is between a wizard and a psion that uses a totally different casting method. There are also more differences there than there are between clerics and druids. So why use this design approach for mages, but not everyone else? By treating all of the mage classes differently, it makes people that like those classes feel marginalized.
Second, this design doesn't accomplish anything. So you put warlocks under mage. But let's say you still give them a different casting method, etc. So why not just make them their own class? What does putting them under the mage label even do, aside from preventing them from ever multiclassing with other mage "subclasses"? And if that is the goal, then why? Maybe a warlock/psion wouldn't be the most popular multiclass combination. But so what? I can't see many people playing a cleric/druid either, and yet that is allowed.
Putting shadowdancers under the rogue, and stuff like that? That's fine. I don't mind them bringing back "prestige classes" this way. I even prefer it. The problem I have is that they're treating wizards, warlocks, psions and artificers just like prestige classes, when those things were main classes before. The artificer, might be okay, as it was more of a niche class to begin with, but this doesn't work well with any of the others. Each of those things have plenty of conceptual room for subclasses of their own. So then you end up with mages having this odd three tier thing, with subclasses within subclasses, something they aren't doing for any other class. It's just nonsensical. This has to be the most misguided thing that they've ever considered doing in Next, IMO.