You've brought up the key piece here, the scope of refurbishment. If engines become a Ship of Theseus problem, then it compromises the idea that age proves a particular engine serial number reliability. I think there's a difference between the design overall being reliable (which I agree RS25 has shown), and lifetime improving a unit's reliability.
For comparison on refurb, a Falcon9 first stage with 9 engines is refurbished for $250k[1], while refurbishing 16 RS25 engines (and building a new engine controller) cost $572M[2]. Shuttle and its components weren't reused, they were rebuilt, and this (probably unfair) cost comparison shows it.
For comparison on refurb, a Falcon9 first stage with 9 engines is refurbished for $250k[1], while refurbishing 16 RS25 engines (and building a new engine controller) cost $572M[2]. Shuttle and its components weren't reused, they were rebuilt, and this (probably unfair) cost comparison shows it.
[1] https://www.elonx.net/how-much-does-it-cost-to-launch-a-reus...
[2] https://oig.nasa.gov/docs/IG-20-012.pdf