I don't mind class exclusive spells. But it... well, I don''t know how to feel about sorcerers and wizards getting their own Eldritch Blasts; feels like it makes them feel a bit homoginous. Though I suppose that's no different from the sorcerrs losing spontaneous magic angle too. Or expertise being an everyone thing, and not a rogue specific thing anymore.
I'm also not quite a fan of making it the mage group feature. Like... you can get Expertise through feats. Weapon Mastery is a feat. Channel Divnity is currently NOT a feat. By definition, class exclusive spells can't be a feat. It also suggests that other classes wouldn't get unique spells, like the bard. Actually, would it be a bad idea for bardic inspiration to be a spell instead of a wannabe-channel-divinity?
I don't mind warlocks getting EB and Hex, though it is curious that they don't get any more unique spells at higher levels like wizards and sorcerer do, though they are getting patron magic and that Contact spell at 11... Wizard ones are... weird. I mean, I don't mind Scribe, Memorize, Modify, Create being spells, but it has some very interesting connotations about how wizardry works that not everyone might like.
Sorcerer magic... honestly, other than it needing tweaking, its not bad. Sorcerous burst is pretty easy to fix - just make it either 2d4 or 2d6 melee range. Pull the random element from Chaos Bolt, roll 3d6; random element can be part of Wild Magic subclass that modifies the sorcerer unique spells. Vitality isn't a terrible idea, just undertuned - its a combo of a two lower level spells, but you rarely benefit from both at once and the amount healed is low. Incarnate is admittedly bad specifically as a spell, and Apothesis is OMG OP, but its not like the ideas aren't salvagable.
We can also change how Elemental Adapt works - instead of treating 1s as 2s (which is actively undesirable now for Eruption), we can change it so that it allows you to change the result of a die up or down by 1. This is, on the face of it, just a +1 damage boost, but for a sorcerer? Burst and Chaos Bolt will get extra damage riders more, Eruption will almost certainly get the condition you most desire.
The main problem with dragon sorcerer is that they're trying to be melee-ranged sorcerer without giving the right tools for it. We get extra AC and health, but no reason to ever be in melee until level 10; kind of why I like the idea of melee Burst. I would also change the dragon's elemental bonus from +CHA to +2d6, and go all in on the d6 rolling. Make dragon breath at 10 a shaped Eruption with free metamagics applied instead of a crappy Burst. Dragon wings need to emphasize the dragon sorcerer playstyle, not be a confusing mix of contrariness. Flyby sorcery attacks, maybe?
Got a bit off track there, but anyways.
TLDR: We can make unique spells work, and work well. Even sorcerer's. But not sure its appropriate as the Mage Group feature.