So, a divine caster like a Cleric, Paladin, Druid etc don't need any actual divine link to power and can just use "The power of my inner belief )or love or friendship or self respect etc) to gain divine powers.
Sure, okay. Let's work with that.
So why would a Warlock ever make a deal with Cthulu or a Fey Princess?
Some possible reasons:
1) The person doesn't have inner belief such that they can access divine powers.
2) There are other powers out there, that are not accessible via inner belief itself, and the character wants them, rather than the divine power.
Another, more metaphysical approach is that, in fact, everyone is already accessing power via that inner belief. All the trappings are merely the frameworks that support that belief. The wizard believes magical power comes from study. The warlock believes that power comes from their patron, and so on.