Take this guy:
Specifically this:
So the redheart insert is glued into an engraved pocket on the underside of the lid, which is a through-cut inlay piece. Alignment was key, so I needed the pocket to be perfectly placed on the underside of the lid. While I may have been able to engrave the two pieces of inlay separately, the chances of getting it right were greatly reduced compared to assembling first, then using a jig to setup the engrave after the glue dried.
So, it’s really situational… but there are definitely cases where engraving after the cut is a good plan.