When to Homebrew
First, let's start with some theory. Ask yourself "why do I want to create this homebrew rule?" Is it because it provides for something the current rules don't, or because it sounds cool to make it? You should have a clear vision for what your rule provides that the existing rules don't.
As far as you flavor goes, Pathfinder's core rules already contain exactly this idea. The Sorceror is a class which explicitly gets its spellcasting power from its heritage. They are born with magical power lurking within them. Your proposed homebrew is redundant with existing options.
Another Issue: Scope
Another consideration might be the difficulty of the proposed rule. Creating a homebrew item, spell, feat, etc. is easier because you haven't touched the underlying rules. In this case you are proposing a change to the fundamental aspects of a character. Any change here will have an influence on nearly every other aspect of a character. Attributes influence class abilities (including spells), skills, saving throws, feats, and more. Are you really ready to re-balance all of those based on your idea?
To be clear you don't just need to re-balance the parts explicitly tied to spellcasting, you need to consider its effect on everything. If a Wizard uses your Magic attribute instead of Intelligence, that will also dramatically decrease their skill points. It will decrease their Intelligence-based skills. They may not qualify for some feats, which explicitly require a base Intelligence score.
All of my campaign settings take place in my own creations. I nearly always tinker with the default races, classes, etc. to fit the world I am creating. Generally, it is much easier to cut published material than it is to add to it. Just tell your players that for flavor reasons, the only full spell-casters available are Sorcerors.