Etch depth is a function of what the die does. A printing plate needs only enough relief to keep the non-image areas clear of the substrate. A foil stamping die needs more, so that the foil is pressed cleanly and the shoulders do not mark. A sculpted belt plate needs considerably more again.

Plate thickness follows from that. The plate has to hold the etched depth and still leave enough material beneath to stay rigid in the press, because a plate that flexes under pressure gives an uneven impression regardless of how well it was etched.

The two also interact with detail through undercut: deeper etching means more time in the bath, which means more lateral loss. A design with very fine detail and a requirement for great depth is a design that needs reconsidering, not a plate specification problem.

Where a job sits at the limit, say so at the enquiry rather than after the first batch. Changing plate thickness is a cheap conversation before production and an expensive one after.