Im rephrasing and reducing this to be a bit to be less confusing:
When would 'eager' be the right mode to use?
When you are Using Deduplication, Compression, or Thin Luns, on your SAN underlying the VMFS Store, instead of or in addition to, using Thin Provisioned VMs.
Usually you would only use this when reclaiming all of the free space in a vmfs volume by creating an extra Disk deployed this way.
Eager Zero is used for zeroing the space used by the VMDK on the VMFS store, and isn't really useful on a deployment of a new VM.
The classic example on why else you might use it was always pretty extreme/niche, and even more so today.
To pre-zero the sectors that will be written to by the VM, so that when the VM is running, it reduces VCPU load and disk write latency when writing 0s to the disk.
However this benefit is only while the VM writes to unused sections of disk, and so applications that were write-once read many would see the largest benefit.