I’m not claiming serial numbers as unique identifiers have no value. Nostr event ids are a useful example. Database indexes another.

It’s more around in day to day life, when did you ever check the serial number on your fiat bank note when someone paid you? Never.

Sure, perhaps that’s hard to look up and easier with a Bitcoin system - however you don’t need to check an ordinal sat number to check if you now hold newly transferred Bitcoin. No Bitcoin wallet has to check the ordinal to verify payment success.

The issue is basically digital goods are fungible (copy + paste, now which is the original? Do you care?). Serial numbers are there to make goods non-fungible (you can’t swap two things and not be able to detect that).

Outcome, Ordinals are just some arbitrary mapping using some statistical uniqueness to apply potential perceived value, which will only ever be intangible, and unless you collect postal stamps, you likely shouldn’t care.

Side note: unless you have a centralised authority that signs the authenticity of an inscribed ordinal, in a decentralised world, inscriptions are lacklustre.