It does not have to be run from the zeros, it has to access the zeros while it’s running (to allocate uids).
You could run the bulk loader from your laptop with a port-forward to the zero leader if you want. The reason I do it in the init container of one alpha is to use the 16c 64GiB ram is has. (we have like 30billion edges in my dgraph cluster now)
But yes, the alphas should be down - otherwise they will do stuff with the zeros while the bulk loader does.