While what you say is true, it seems to me like what you're describing isn't quite the same definition of causality being infinitely fast.
The fact that causal effects happen in the next tick means some minimal time has passed. So in your definition causality can cover the entirety of a finite universe in an incredibly short amount of time (one tick). But it seems like that's not the same as covering the entirety of a finite universe in zero time. In that case, every result would happen within the same tick as its cause.
There's more than one way to "implement a universe", but one hypothetical way to run a simulation is to alternate the simulation of forces and effects/causes.
A simulation could use particles with attributes like position, velocity, and also a "sum of forces". Then each update has the following steps:
1. Reset the sum of forces for all particles to zero.
2. For all particles, add the contribution to the forces on it from all other particles.
3. For all particles, update the next particle position based on the collected forces.
In the above, there's no intermediate state between updates, everything moves to the next position synchronously from the perspective of in-universe observers. (The external simulation can update particles one-at-a-time, but this is not an "observable" inside the simulation.)
While what you say is true, it seems to me like what you're describing isn't quite the same definition of causality being infinitely fast.
The fact that causal effects happen in the next tick means some minimal time has passed. So in your definition causality can cover the entirety of a finite universe in an incredibly short amount of time (one tick). But it seems like that's not the same as covering the entirety of a finite universe in zero time. In that case, every result would happen within the same tick as its cause.
There's more than one way to "implement a universe", but one hypothetical way to run a simulation is to alternate the simulation of forces and effects/causes.
A simulation could use particles with attributes like position, velocity, and also a "sum of forces". Then each update has the following steps:
1. Reset the sum of forces for all particles to zero.
2. For all particles, add the contribution to the forces on it from all other particles.
3. For all particles, update the next particle position based on the collected forces.
In the above, there's no intermediate state between updates, everything moves to the next position synchronously from the perspective of in-universe observers. (The external simulation can update particles one-at-a-time, but this is not an "observable" inside the simulation.)
The cellular automata view of reality is entirely compatible with what I said.