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.
Current Options
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.
Alternatives
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.