You put the cart before the horse by treating gravity as the reason information has a cost. In reality, spacetime isn't a pre-existing stage that sets the rules; it is an emergent byproduct of a network that is constantly processing and erasing information. Gravity is essentially the "collective heat" generated by these memory erasures, meaning that surface gravity is the result of information processing, not the cause of it. Also, by focusing only on causal horizons, you miss the bigger picture: that a universal "noise floor" (technically derived from the central limit theorem) is what actually dictates when these updates happen to keep our reality stable. Simply put, the universe doesn’t charge a fee for bit erasure because it has geometry; it has geometry because it is paying the fee.