A high intelligence prepared caster can achieve their power through study and practice, just like Wizards. That's one of the reasons I liked Witch in PF1, because they could learn spells like a Wizard but had a distinct way of going about it. That is, learning more esoteric, bizarre spells gleaned from old rituals, hags, hedge magic, and bits of handed down lore. The Occult spell list does a great job at this.
Patrons never felt particularly important to the concept of a witch to me. Partly because I'd like it if you can play a "christian boogeyman witch" as well as a version of the "wiccan witch", which certainly doesn't need a patron.
Also, the etymology of the word Patron goes...
I still disagree with this to a degree.
Looking specifically at the Pathfinder Witch specifically and not just the generic concept of a Witch, yes a Witch is an INT caster and thus improves their magic through practice and study, but the magic in question is only accessible through the Patron via the Familiar. Hence why the Familiar acts as the Witch's spellbook and teacher.
A Witch that solely learns their magical abilities themselves with no Patron at all isn't a Witch, they're a Wizard. Sure, you can argue that the Witch delves into more esoteric and unknown magics, but the difference in that is basically just academic. There is no reason a Wizard can't go about studying older and forgotten rituals. Heck, in doing so they could even have a feat or even a whole archetype that lets them take some spells from the Occult Spell list.
The thing that makes the Witch thematically different IS the Patron. Even if that Patron can more or less be ignored during gameplay (just like how if you are playing a Wizard, you don't need to roleplay out the intense study during downtime in order to learn a new spell). If you want to play a Winter Witch, there is no reason at all that at your table you can't say "Hey, I don't really want to deal with Baba Yaga and her craziness, so can I just say that I am learning from the essense of Winter itself?". But that is still a Patron. You are still being tied to that Patron through your familiar and drawing knowledge from it. A Patron doesn't NEED to be a singular entity. It just needs to be some outside power that you can make a pact with.
And yes, I get that in PF2, they have stated a desire to move towards Patrons that are defined individuals rather than nebulous and unknown entities, but that is just flavor-text. There's no reason you can't decide that it works that way for your table.
As a final note, the etymology of Patron thing is a non-starter. Patron doesn't mean that anymore. Words change and evolve over time. Patron doesn't refer specifically to a father figure any more than ambidextrous means that you are untrustworthy or two-faced (which was the original terminology of the word, and MUCH more recently than Patron used to refer to father).