I'm confused? Serial means "always increasing and having no holes" -- it's one thing after the other. What you're arguing for sounds like just IDs, not serial IDs.
Well, by your definition what people use as serial IDs isn't serial.
Databases have the concept of sequences, that are closer to your definition, but make no promises about holes (they normally don't generate holes by themselves, but there is no way to guarantee you won't lose numbers upon usage). It is common to use sequences to feed serial IDs, but not all DBMS do that and it's not a requirement in any way.
