Hypothetically the code is consolidating sites where allocation happens. Zig’s design seems to really push you toward this by making anything else a PITA. So then that allocator reference is being used frequently and already sitting in a register anyway.
The few extra instructions for explicitly passing it might be small compared to the cost of having objects carry their own references. That would grow each instance by ~8 bytes. It would mean that the pointer to the allocator needs to be pulled from a unique memory location for each instance, which is maybe an order of magnitude slower than already having it in a register. Larger data structures would also mean more cache misses, which are another order of magnitude slower.
And this is all chicken feed compared to actually taking a walk of shame out to the DRAM to fetch more memory. So the language ergonomics encouraging you to consolidate your allocation might trump all other considerations in practice.