But the cryptographic bottleneck is in HSMs, not in database servers (database servers don't generate the digital signatures, they just have to store them after they've been generated).

Bitcoin is actually not limited by compute power at all. Its an artificial cap on transaction rate to prevent the blockchain from expanding too large and preventing normal users from hosting the whole thing.

You can see the blockchain size was growing exponentially but then switches to linear as we hit the transaction cap and it now sits at about 350GB