After some thinking about metamagic I'm wondering why it have sorcerers and no wizards?
As I understand wizards as men who learning how to use, handle, work with magic in the smallest details. Then it made me a sense to give them the ability to made theirs spell empowered, quickened, subtle,... They know how they work then they should know how to change them.
Sorcerers "cast just for fun" Nobody teach them, they can be really stupid, but hey they can change spell "at will".
I'd like to see metamagic for wizards and sorcerers got something more from their ancestry. Be much powerfull in close segment of their magic (elemental magic for dragon ancestry, choosing wildmagic effects for wildmagic sorcerers etc.)
The real reason is separating the roles of Wizard vs Sorcerer.
If you start thinking in terms of "makes sense" you can really do the same for the Sorcerer: she is an
innate spellcaster, meaning she is
actually magical, doesn't need to study or be taught, so why shouldn't she be able to just research new spells and increase her number of spells known for a small cost like a Wizard? Makes sense! And why shouldn't she be able to pick on everybody's spells list, like a Bard? Makes sense! And why does Wizard and not Sorcerer get Signature Spell and Spell Mastery, obviously a Sorcerer is more likely to develop those after casting the same friggin' only 15 spells all her life... makes sense!
And why not saying that Wizards can be really un-charismatic, why being intelligent should give you an edge on magic which is the
opposite of science in so many ways, magic should be about "soul" and personal magnetism and sense of self (reality check: compare real-life scientists with real-life "practitioners" of magic).
If you want your Wizards to be more "uber" like in older editions, then just get rid of the Sorcerer class and give everything to your Wizards. This is what they did in 3.5ed anyway, they murdered the Sorcerer class by making its unique stuff available to others.
So yeah, the real reason
not to give metamagic to anyone else is because it's the only mechanical element that makes Sorcerer a class on its own (Sorcery Points don't really do it, not enough at least). Just like you also don't want everything of the Fighter to be available to everyone otherwise nobody will ever play a single-class Fighter again.