Where exactly is my logic funny? Mined blockchains scale linearly. Increasing block size, etc. can increase speed temporarily but can still only scale linearly. Busy site or not, the ledger needs an architectural change to handle exponential growth. Your busy Postgress db would also need to change in architecture from a single resource to something more distributed in order to scale exponentially. A less busy website of the same architecture also wouldn't handle exponential growth. What am I missing?

Edit: To clarify, yes, some mined blockchains feel faster now simply because they are less busy. They are still doomed to Bitcoin's fate at scale unless distributed systems techniques like sharding (or Nano's block lattice) are used. I'm not saying that the less busy blockchains are any better.